Coming from latest 3.x, I tried to upgrade to 6.2.9.
Up until DB version 403, the DB updates succeeded.

I get a warning then, "Theme '%s' has been uninstalled because it's not compatible with this LimeSurvey version."

This was expected, as the manual at https://manual.limesurvey.org/Major_version_upgrade mentions it ("All custom survey themes (this includes extended themes) will be uninstalled..".

The message is therefore correct, it just seems it did not actually get uninstalled, as the browser returns to the exact same page.
Enabled debug=2 and debugsql=1 in config.php, but no errors logged whatsoever.

application/models/TemplateConfig.php
916 public static function validateTheme($themeName, $themePath, bool $redirect = true): bool
917 {
918 // check compatability with current limesurvey version
919 $isCompatible = TemplateConfig::isCompatible($themePath);
920 if (!$isCompatible) {
921 self::uninstallThemesRecursive($themeName);
922 if ($redirect) {
923 App()->setFlashMessage(
924 sprintf(
925 gT("Theme '%s' has been uninstalled because it's not compatible with this LimeSurvey version."),
926 $themeName
927 ),
928 'error'
929 );
930 App()->getController()->redirect(["themeOptions/index", "#" => "surveythemes"]);
931 App()->end();
932 }
933 }

calls App()->end();

This seems to be the cause for .. well, the update to end :-)

If I comment lines 930 and 931, the DB upgrade finishes and LS seems to be usable. The mentioned theme is then indeed listed with an error that it is not compatible (but it is not below "Deprecated survey themes").