Here is my suggestion:

1. place the profile wherever you wish
2. click help>troubleshootinginformation
3. scroll down to 'profiles' and click 'about:profiles'
4. click the 'create profile ' button
5. click next
6. now, at this point, FIRST enter a shortcut name such as MYPROFILE
7. then, afterwards, click the 'choose' button and locate and select the profile you placed and launch it

Thank you for your reply. However, what you describe is exactly what I already tried before. I checked again, because you stressed the importance of first entering a name for the new profile and then choosing the folder where it is located. Unfortunately, this changes nothing about the problems and error messages I described above. Maybe there are other ideas what I could do ...?

That should have set the profile as default. Click help>troubleshootinginformation, scroll down to 'profile folder', click 'open folder' and check to see if the profile location is the one you set. If so, your profile is being loaded, but there are problems with it. The steps I suggested would have loaded a profile, so I'm puzzled. Worst case, you could edit the profiles.ini to point to it.

The profile folder is correctly set to /home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default according to the troubleshooting information.

about:profiles also tells me that it's the default profile.

Well, I already tinkered with profiles.ini before posting my original query, but I find it puzzling. Here's what it looks like after I followed the above mentioned steps and your recommendations (without any manual changes):

[General] StartWithLastProfile=1 Version=2

[Profile1] Name=default IsRelative=1 Path=626v5u50.default Default=1

[Profile0] Name=default-esr IsRelative=1 Path=nhaprh97.default-esr

[InstallFA9DEAB4CC8E0E14] Default=/run/user/1000/doc/e9915464/tj63nudj.default Locked=1

[Profile2] Name=Torben IsRelative=0 Path=/run/user/1000/doc/e9915464/tj63nudj.default

As far as I understand, this suggests that 626v5u50.default is the default and not tj63nudj.default aka "Torben". And it seems that the path for "Torben" is not home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default (although the trouble shooting information says so and Thunderbird obviously does find all the old mails stored there) but /run/user/1000/doc/e9915464/tj63nudj.default (what the profile assistant told me in the first place, see original post).

I don't know what to make of this ... :-/

On the new computer, I want to put the profile into a custom folder, not the standard folder (which would be /home/torben/.var/app/net.thunderbird.Thunderbird/.thunderbird in my case)

Since you're running the TB Flatpak version, stick to the path above. A Flatpak app is executed inside an isolated environment called a sandbox with minimal host access.

If you don't like the path above, don't use the Flatpak version.

Ok thank you, christ1. Here it shows that I am a Linux newbie. ;-)

In what way should I install Thunderbird then?

When I choose the RPM version, the error messages are more or less the same ... or even worse: I cannot run my newly created profile from the about:profiles tab; and restarting Thunderbird directly causes the error "Thunderbird is already running, but is not responding. To use Thunderbird, you must first close the existing Thunderbird process, restart your device, or use a different profile." ..

What is the contents of your profiles.ini file? Note, profiles.ini resides at ~/.thunderbird. This is also the path where your profile should be located.

restarting Thunderbird directly causes the error "Thunderbird is already running, but is not responding.

See https://kb.mozillazine.org/Profile_in_use

When I follow the steps in my original post (using RPM instead of Flatpak), these are the contents of profiles.ini before the step "Create new profile ...":

[Profile1] Name=default IsRelative=1 Path=xlkzpqp3.default Default=1

[Profile0] Name=default-esr IsRelative=1 Path=2r5eow37.default-esr

[General] StartWithLastProfile=1 Version=2

[Install3DDF446CE6CB1A45] Default=2r5eow37.default-esr Locked=1

After adding the existing profile file in the custom location, this is how it looks like:

[Profile2] Name=Torben IsRelative=0 Path=/home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default

[Profile1] Name=default IsRelative=1 Path=xlkzpqp3.default Default=1

[Profile0] Name=default-esr IsRelative=1 Path=2r5eow37.default-esr

[General] StartWithLastProfile=1 Version=2

[Install3DDF446CE6CB1A45] Default=/home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default Locked=1

Besides, I tried to work through the help article -- thank you for the link.

When I run thunderbird from the terminal (directory seems to be /usr/lib64/thunderbird ?) with the following command:

thunderbird --profile /home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default

I get the familiar error message "Thunderbird is already running, but ...". I suppose this means that the problem is not in the profiles.ini file?

When I run thunderbird from the terminal (directory seems to be /usr/lib64/thunderbird ?)

Typically 'thunderbird' is located in a 'bin' directory, and those should be in the PATH environment variable. I doubt that /usr/lib64 is the correct path.

... with the following command: thunderbird --profile /home/torben/Dokumente/Gemeinsam/Documents/Briefe/Thunderbird_Profiles/tj63nudj.default

The correct command would be: thunderbird -P Torben

Thank you for your reply.

Typing

thunderbird -P Torben

results in the same error message. Should we still look into profiles.ini or what would you suggest?

While Thunderbird is closed, remove the profile lock file as per the support article linked above.