This should allow copying too? 

Yes. When text is selected, it should allow [Cut | Copy | Paste | Paste and Go] 
When no text is selected and there is something in the clipboard [Paste | Paste and Go] 

Does that make sense ?

Comment #3 is a little confusing. Here is the breakdown for the three edit menus we should be showing in the new omnibox:

1/ Unfocused (steady-state): Copy [Paste and Go]
2/ Focused with selection: Cut, Copy [Paste, Paste and Go]
3/ Focused with no selection: Select, Select All [Paste, Paste and Go]

...where square brackets denote optional actions dependent on the presence of text/URL data in the clipboard.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/2b8fd19bad139dd44c8ee5eb496f43d79fdea128

commit 2b8fd19bad139dd44c8ee5eb496f43d79fdea128
Author: stkhapugin@chromium.org <stkhapugin@chromium.org>
Date: Fri Jun 08 17:10:35 2018

Fix tests with Refresh Location Bar flag ON.

Fixes the tests broken by enabling the refresh location bar, introducing
helpers as necessary.

Bug:  834345 ,  821821 
Cq-Include-Trybots: luci.chromium.try:ios-simulator-full-configs;master.tryserver.chromium.mac:ios-simulator-cronet
Change-Id: Ifb767a192c3f4d3f35bf4714768352a83d4a1d99
Reviewed-on: https://chromium-review.googlesource.com/1070147
Commit-Queue: Stepan Khapugin <stkhapugin@chromium.org>
Reviewed-by: Rohit Rao <rohitrao@chromium.org>
Cr-Commit-Position: refs/heads/master@{#565664}
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/browser_view_controller_egtest.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/location_bar/location_bar_steady_view.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/popup_menu/BUILD.gn
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/popup_menu/popup_menu_mediator.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/reading_list/BUILD.gn
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/reading_list/reading_list_egtest.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/ui/toolbar/toolbar_egtest.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/web/browsing_egtest.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/browser/web/cache_egtest.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/test/earl_grey/chrome_earl_grey_ui.h
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/test/earl_grey/chrome_earl_grey_ui.mm
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/test/earl_grey/chrome_matchers.h
[modify] https://crrev.com/2b8fd19bad139dd44c8ee5eb496f43d79fdea128/ios/chrome/test/earl_grey/chrome_matchers.mm

This doesn't seem as important as other bugs; dropping to P2 unless you object

This looks like it's been started, no?

Changing bug name to reflect contents more accurately.

 Issue 730663  has been merged into this issue.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/b84517914ade8aec09ebfffec8e1198311faae08

commit b84517914ade8aec09ebfffec8e1198311faae08
Author: Elodie Banel <lod@google.com>
Date: Fri Jul 20 14:02:53 2018

Update editing menu in focused omnibox.

Update editing menu in focused omnibox. Expected behavior now is:
If there is pasteboard data, show "Paste" and "Paste and Go"
If there is selected text, show "Cut" and "Copy"
If there is no selected text, show "Select" and "Select All".
Side note: This CL does not fix issue 864984.

Bug:  834345 
Cq-Include-Trybots: luci.chromium.try:ios-simulator-full-configs;master.tryserver.chromium.mac:ios-simulator-cronet
Change-Id: If1fb9c29258caca80f96f9cb2dfe5ba4893803d9
Reviewed-on: https://chromium-review.googlesource.com/1143279
Reviewed-by: Justin Cohen <justincohen@chromium.org>
Reviewed-by: Stepan Khapugin <stkhapugin@chromium.org>
Commit-Queue: Elodie Banel <lod@chromium.org>
Cr-Commit-Position: refs/heads/master@{#576850}
[modify] https://crrev.com/b84517914ade8aec09ebfffec8e1198311faae08/ios/chrome/browser/ui/omnibox/omnibox_coordinator.mm
[modify] https://crrev.com/b84517914ade8aec09ebfffec8e1198311faae08/ios/chrome/browser/ui/omnibox/omnibox_text_field_ios.mm
[modify] https://crrev.com/b84517914ade8aec09ebfffec8e1198311faae08/ios/chrome/browser/ui/omnibox/omnibox_view_controller.h
[modify] https://crrev.com/b84517914ade8aec09ebfffec8e1198311faae08/ios/chrome/browser/ui/omnibox/omnibox_view_controller.mm

Do you need to cherry-pick this once it's verified? 

Issue 862739 has been merged into this issue.

This bug requires manual review: Less than 28 days to go before AppStore submit on M69
Please contact the milestone owner if you have questions.
Owners: amineer@(Android), kariahda@(iOS), cindyb@(ChromeOS), govind@(Desktop)

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

Hi lod@: For M69 we are targeting P1, Proj-UIRefresh bugs only since we're already merging so much for this milestone. I'm rejecting merge per c#7. Reach out to marq@ if you think this is a mistake.

What happens currently if you long press on the omnibox, if we don't take this CL in 69?  Is this an important quality-of-life fix, or would it be ok to ship without this?

It seems like  crbug.com/870329  is what happens, and that is marked P1. 

Yep, what stk said. I think this fix is worth prioritizing because of this empty-paste bug.

This bug requires manual review: Less than 23 days to go before AppStore submit on M69
Please contact the milestone owner if you have questions.
Owners: amineer@(Android), kariahda@(iOS), cindyb@(ChromeOS), govind@(Desktop)

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

 Issue 870329  has been merged into this issue.

Raising this to P1 since  crbug.com/834345  that was duped into this was P1. 

Ok, canary verification please.

Verified in 70.0.3517.0 canary. The feature works correctly, bug on iPad where URL is blank on "Paste and Go" does not repro.

Reassigning to stk to handle potential merge since I am leaving the team. Thanks.

Approved. Please merge asap.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/49a3dd7f4b45759d7e3ad3297cd402dbb589f707

commit 49a3dd7f4b45759d7e3ad3297cd402dbb589f707
Author: stkhapugin@chromium.org <stkhapugin@chromium.org>
Date: Mon Aug 13 16:18:03 2018

Update editing menu in focused omnibox.

Update editing menu in focused omnibox. Expected behavior now is:
If there is pasteboard data, show "Paste" and "Paste and Go"
If there is selected text, show "Cut" and "Copy"
If there is no selected text, show "Select" and "Select All".
Side note: This CL does not fix issue 864984.

TBR=lod@google.com

(cherry picked from commit b84517914ade8aec09ebfffec8e1198311faae08)

Bug:  834345 
Cq-Include-Trybots: luci.chromium.try:ios-simulator-full-configs;master.tryserver.chromium.mac:ios-simulator-cronet
Change-Id: If1fb9c29258caca80f96f9cb2dfe5ba4893803d9
Reviewed-on: https://chromium-review.googlesource.com/1143279
Reviewed-by: Justin Cohen <justincohen@chromium.org>
Reviewed-by: Stepan Khapugin <stkhapugin@chromium.org>
Commit-Queue: Elodie Banel <lod@chromium.org>
Cr-Original-Commit-Position: refs/heads/master@{#576850}
Reviewed-on: https://chromium-review.googlesource.com/1172781
Cr-Commit-Position: refs/branch-heads/3497@{#564}
Cr-Branched-From: 271eaf50594eb818c9295dc78d364aea18c82ea8-refs/heads/master@{#576753}
[modify] https://crrev.com/49a3dd7f4b45759d7e3ad3297cd402dbb589f707/ios/chrome/browser/ui/omnibox/omnibox_coordinator.mm
[modify] https://crrev.com/49a3dd7f4b45759d7e3ad3297cd402dbb589f707/ios/chrome/browser/ui/omnibox/omnibox_text_field_ios.mm
[modify] https://crrev.com/49a3dd7f4b45759d7e3ad3297cd402dbb589f707/ios/chrome/browser/ui/omnibox/omnibox_view_controller.h
[modify] https://crrev.com/49a3dd7f4b45759d7e3ad3297cd402dbb589f707/ios/chrome/browser/ui/omnibox/omnibox_view_controller.mm

There is still a TODO in the code for disabled testCopyPasteURL, which refers to this bug.