I think you misunderstand Nico's concern. He want's to update from 2.3.4 to 2.3.5 because of the conversion of the database functions. Your tip to use the current update file (update_2.3.5-2.4.php) will not work because at first it will fail for a source version below 2.3.5 and at second it did not exist in the sources for version 2.3.5.
I never saw an error with the update to version 2.3.5. On the other hand the update does not change anything in the database with the exception of the version string. Last changes in the database itself was performed with the update to 2.3.0 (see therefore the if-statement in line #549).
My assumption is that Nico or his hosting provider runs PHP7.x on the webserver. PHP7 no longer know the functions of the old myslq-lib and because in version 2.3.5 the only query to perform is the one to reset the version string, the script fails exactly at that point. On the other hand the version 2.3.4 should not be able to run a single mysql-function.
@Nico: To update from version 2.3.4 to 2.3.5 you can upload all files that are specified in the list for version 2.3.4. Afterwards you have to set the version number to "2.3.5" in the settings table.
On the other hand it should be a simpler solution to install version 2.3.7 and to import the content of the old forum. There is only one relevant change in the settings table in version 2.3.7 you have to checkafter moving the settings from the old to the new forum. Search for the setting
temp_block_ip_after_repeated_failed_logins and set it to a value of 10 minutes in the case it has in reality a value different from
0. (see therefore the wiki page about the configuration settings)
From version 2.3.7 you should be able to update directly to the current version 188.8.131.52.
Trenne niemals Müll, denn er hat nur eine Silbe!