Why is my time machine backup so large after updating from OSX 10.13.6 to 10.15.4?
First off I can definitely say that the large backup is not caused by the drop of support for 32-bit applications, nor is it due to yet another change of file system from APFS to "something new" (note that Apple used HFS+ for ~20 years before moving to APFS, so file system changes are definitely not done often).

One of the big changes that comes with the update from 10.13 to 10.15 is ofcourse the operating system files themselves. Most of them have changed in some way, so that contributes a lot to the difference. Also Catalina split system and other data over two volumes (while preserving a unified view) so that to a backup system some files could seemingly have moved around.

I can't immediately find a reason for Photos to have made changes to your originals. I would suggest comparing one or two photos in the backups from before and after your upgrade to find the differences - perhaps there has been some kind of meta data change, but I haven't experienced that when upgrading to Catalina.

In general you can use a tool such as BackupLoupe to examine the Time Machine backup made just after upgrading to figure out, which files were changed/moved and made the backup larger.

Another tool that can be used is GrandPerspective, which will visualise the data taking up space in the backup, allowing to you get a high level overview of what taking up the most space.