Server is Baikal 0.4.6 (flat)

Do you have write access on that calendar?
Perhaps Connector tries to sync a change made in Thunderbird to the server, which fails.
That could stop synchronization in Thunderbird.

I have some information which might relate to the Photo issue. I have a nextcloud setup (fork of owncloud). I use this to sync contacts between Thunderbird on my desktop and DavDroid on my phone.
I can create contacts in Sogo/Thunderbird and they are uploaded correctly. I am able to add or edit text fields in the web interface of nextcloud or DavDroid and those are synced across. However any changes to the Photo on the web interface or in Davdroid, result in the photo being deleted in Thunderbird. I believe I've traced this down to the different versions of the VCF format. They differ in the way they handle the PHOTO field. eg.
VERSION:3.0
PHOTO;ENCODING=b;TYPE=JPEG:/9j/4AAQSkZJRgABAQAAAQABAAD/blahblah
VERSION:4.0
PHOTO:data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD/blahblah

So what's happening, as far as I can see is that Sogo talks 3.0, so uploading to the server and down to Davdroid is working. Davdroid sends it back as 4.0, which nextcloud can also cope with, but Thunderbird/Sogo can't, so it ignores the photo tag and just imports the rest.

Perhaps there are also other issues with 3.0 vs 4.0?

Hope this helps. I looked in the Sogo Connector github page for somewhere to leave this information, but this seemed like a more likely place.

Many fixes pushed recently - try a nightly build: https://packages.inverse.ca/SOGo/thunderbird/nightly/