Please resubmit from the 5.3.x branch, because an associated Jira task is for the 5.3.x branch as well.

In D519#10607, @erik wrote:

Part 2 - "confirm, that you're seeing an Admin Console" - no, adding test code to OnLogin prevents from login to the adm.console.

Boyscout improvements in session.php

Part 2 - "confirm, that you're seeing an Admin Console" - no, adding test code to OnLogin prevents from login to the adm.console.
Part 3 - "replace the tab URL with the provided URL (text after #redirect#)" - seems, missing some action and/or confirmation after this step ot the test plan

Applying the Boyscout Rule principe.

In D518#10578, @erik wrote:

Today I have z-index; 0; in DIV Can't provide screenshot without -index today.

Today I have z-index; 0; in DIV Can't provide screenshot without -index today.

In D518#10573, @erik wrote:

Part 2 - all right, so revision is accepted.

Added reference to the used code origins.

done all requested code improvements

Update test plan to cover requested changes as well.

In D513#10483, @erik wrote:

Part 3.1.1 login to the Admin Console by accessing it on the sd1.test.domain.com domain over http:// protocol - FAILED, after login attempt - redirect to the login page. SUCCESS after cookies deleted (beyond test plan)
Part 3.1.12 confirm, that orange buttons for editing page/content blocks are now shown - NOT STABLE. At first attempt - no orange buttons. Then I logged in from main domain, set Default theme as primary theme, checked that orange buttons shown, restored Advanced theme as primary theme, then tried again login to sd1 domain, failed, cleared cookies, login to sd1 admin - and only then orange buttons shown

In D511#10453, @erik wrote:

Part 3.2 go to the Configuration → Website → Advanced section - FAILED, can't. login, redirects to login screen. Logged in only after all current site cookies deleted before login.

Part 3.1.1 login to the Admin Console by accessing it on the sd1.test.domain.com domain over http:// protocol - FAILED, after login attempt - redirect to the login page. SUCCESS after cookies deleted (beyond test plan)
Part 3.1.12 confirm, that orange buttons for editing page/content blocks are now shown - NOT STABLE. At first attempt - no orange buttons. Then I logged in from main domain, set Default theme as primary theme, checked that orange buttons shown, restored Advanced theme as primary theme, then tried again login to sd1 domain, failed, cleared cookies, login to sd1 admin - and only then orange buttons shown

Added some explanatory comments.

In D513#10467, @erik wrote:

Part 3.1.7 confirm that [SD ID: 1] is added in the current page blur bar (the 1 is site domain ID) - NO, [SD ID: ] is added. And this is right, because at Preparations 10 "add 1st site domain with: Domain Name=sd1-http.test.domain.com", not sd1.test.domain.com
Part 3.1.9 confirm, that you'll see [Site Domain ID: 1] text (the 1 is site domain ID) - NO I see [Site Domain ID: 0]

Part 3.1.7 confirm that [SD ID: 1] is added in the current page blur bar (the 1 is site domain ID) - NO, [SD ID: ] is added. And this is right, because at Preparations 10 "add 1st site domain with: Domain Name=sd1-http.test.domain.com", not sd1.test.domain.com
Part 3.1.9 confirm, that you'll see [Site Domain ID: 1] text (the 1 is site domain ID) - NO I see [Site Domain ID: 0]
Part 3.1.12 logout - FAILED, infinite redirect to http://sd1.test.domain.com/SVN/5.3.x/admin/index.php?env=-index%3Am0--default---&expired=1 happens
Part 3.2.2 confirm that you're looking at Admin Console at the test.domain.com domain over https:// protocol - NO, I'm looking at Admin Console at the sd1.test.domain.com domain over https:// protocol
Part 3.2.3 confirm that [SD ID: 1] is added in the current page blur bar (the 1 is site domain ID) = NO, [SD ID: ] is added in the current page blue bar
Part 3.2.5 confirm, that you'll see [Site Domain ID: 1] text (the 1 is site domain ID) - NO I see [Site Domain ID: 0]
Part 4.2 confirm, that you'll see [Site Domain ID: 1] text (the 1 is site domain ID) - NO I see [Site Domain ID: 0]
Part 4.4 confirm, that you'll see [Site Domain ID: 1] text (the 1 is site domain ID) - NO I see [Site Domain ID: 0]

Part 3.2 go to the Configuration → Website → Advanced section - FAILED, can't. login, redirects to login screen. Logged in only after all current site cookies deleted before login.
Part 7.9 confirm, that domain/protocol combo is allowed - NO The "https://front-https.test.domain.com" protocol/domain combo is not allowed.
Part 10.2 login - FAILED, can't. login, redirects to login screen. Logged in only after all current site cookies deleted before login.

Excluded "site_domain_eh.php" with no changes from the Differential Revision.

Restored Browse Mode support when Front-End and Admin Console are using different SSL domains.

Discovered a bug where Front-End can’t be opened in a Browse Mode if SSL is being used and Front-End and Admin Console are using different SSL domains.

Updated test plan. Please retest.

In D511#10419, @erik wrote:

All tested, there is list of possible differences from test plan expectations.

Part 2.7 confirm you stayed on the admin1-https.test.domain.com domain and http:// protocol - NO, STAYED ON same domain/protocol test.domain.com

All tested, there is list of possible differences from test plan expectations.

Ensure new identical field order in both unit config and database table.