Only drives in reverse

That should be a Jatco JF506E transmission. They commonly have an issue where they lose reverse but have all the forward gears, to see one the opposite way is rare but not impossible. The most common reason for loss of all forward gears it is a broken retainer clip on, or the outright failure of the low clutch drum.
The same trans was used by VW as the 09A, if you google 09a self study guide 232
you can get a pretty good idea of what you are facing inside.

Thank you.
Is a low clutch drum something a home mechanic can buy and install?

You will need to get it from a transmission shop or order it online unless you have a commercial account at most of the chain parts stores but it can be purchased. However, unless this is a fix it and flip it fast deal I would probably do a full upgrade on it, they are known for the reverse piston cracking the drum failing and the band failing, you can get all of those parts as an upgrade kit that makes that transmission a lot better.

I see information about the reverse piston cracking and that it can be replaced without removing the transmission. Is it possible it has just a cracked reverse piston? Most threads do not mention my symptom, they all have a no reverse condition.
The parts you mentioned are they also all accessible by removing the transmission wind cover?

That should "read end cover".
(I have seen a pictorial breakdown of the reverse piston removal and it looks do-able.

The reverse piston will cause slipping or poor engagement in all gears, but to lose all forward gears but still have reverse only the low drum is the culprit, or its retaining clip.
Should be able to do all of it through the end cover as it provides the access.

Thank you very much.

You are welcome. Thank you for using 2CarPros.

I usually use specific forums. I am impressed and surprised how good the answers were I got here. I will be back.

Steve W. is one of our best! Please use 2CarPros anytime we are here to help.

Cheers, Ken