Is this something that can be reproduced?

@gabrieljenik I can reproduce this. Using our local dev env I have upgraded from 3.x-LTS branch to 5.x branch and then to master.
The last step produced this (see screenshots).

Screenshot 2023-08-14 at 14.08.01.png (60,048 bytes)   

Screenshot 2023-08-14 at 14.08.01.png (60,048 bytes)   

Can you run it with dbug =2 as to see the full failing sQL?

As already mentioned in the description of the ticket:
Using debug=2 I saw that the issue was with command UPDATE "lime_settings_global" SET "stg_value"=:stg_value WHERE stg_name='DBVersion'

As already mentioned in the description of the ticket:

Yes, but now we can see the full stack and the value of the stg_value parameter

Can you please include the full contents of the screen?
The whole dump. You can try printing as pdf.

From here: https://stackoverflow.com/a/13103690/1392917

The reason you get this error is because you have entered a transaction and one of your SQL Queries failed, and you gobbled up that failure and ignored it. But that wasn't enough, THEN you used that same connection, using the SAME TRANSACTION to run another query. The exception gets thrown on the second, correctly formed query because you are using a broken transaction to do additional work. PostgreSQL by default stops you from doing this.

I would say to try this.
Before running the last upgarde, please update the file application/helpers/update/updates/Update_605.php
Remove the try catch structures.
If that works, it means we need to find another way to check if the index exists.

Ex:

if(($this->db->getTable('{{xxxxx}}')->hasIndex('uniqueindex')){
....
}

I removed the try/catch from update, still getting an error, just different.
The issue now is:
CDbCommand failed to execute the SQL statement: SQLSTATE[42P07]: Duplicate table: 7 ERROR: relation "lime_idx1_quota_id" already exists. The SQL statement executed was: CREATE INDEX "lime_idx1_quota_id" ON "lime_quota_languagesettings" ("quotals_quota_id")

Screenshot 2023-08-15 at 13.24.09.png (65,297 bytes)   

Screenshot 2023-08-15 at 13.24.09.png (65,297 bytes)   

OK, great. it worked as expected.

it means we need to find another way to check if the index exists.

Master: https://github.com/LimeSurvey/LimeSurvey/pull/3370

@tibor.pacalat this should be testes with mysql (and mssql) as well

@tibor.pacalat this should be tested added manually the index before update …

Tested and merged.

Fix committed to master branch: http://bugs.limesurvey.org/plugin.php?page=Source/view&id=35484

Fix committed to master branch: http://bugs.limesurvey.org/plugin.php?page=Source/view&id=35483

Fixed in Release 6.2.7+230918