Clarify What Help I need

I have been working with this website for a few years just for purposes of archiving this artist’s work. It is not a priority to the artist to update the website but I’m finding some functionality really challenging because the original site was made in 2014 with the twenty thirteen theme and a custom child theme. I don’t know enough backend to fix things that need fixing, but I’d love to be able to use the newer features that are more drag and drop style to update some of the pages but I keep running into issues that are slightly beyond me. Is there a way to update to a different / newer theme without crashing the whole thing and without completely remaking it? The problem, I believe is that the original designer made custom post types and those aren’t compatible with newer functions.

What I want to do specifically is put photographs on each page into Galleries but this doesn’t seem to be possible in the current state. I think at some point, someone tried to connect to Flickr but this ended up not being used. The photos are mostly just inserted on the page in various sizes.

I am lost as to what I should update, if this qualifies as an entire web update that needs a specialist or if this is something I could tackle in a few hours with some support? Can some just help me figure out how to start on this path? Google has brought me to rabbit holes that make me feel like I need to learn backend design to conquer this, and that just isn’t the solution I need.

The page I need help with: [log in to see the link]