Something like Canva templates
What if you consider... Canva?
You can upload files, that can be the base file, probably the background, and then someone just log in and edit the file? It also has something like Canva for teams, which I have not used, but there it is for a reason.
every month their web banner may have updated text
Some other options can be: files on a shared drive or dropbox, google docs using a presentation, a web-based system that takes the text from a text file and renders an html5 banner, etc.
Software is a relative thing. Again, use Canva, or google docs, or PowerPoint, or maybe Gimp, or someone should learn how to use Indesign and InCopy, or download a PHP script to read txt files, use a FTP client, or pull data from a web form and database...
You could implement a ton of things... but every system needs capacitation and time to implement it.
with a focus on their marketing materials
But if the company really wants "marketing materials" aka "Effective marketing materials" they should have a "marketing person". If the company is small, they probably should hire a freelancer, which is probably you.
If the marketing material is reusing the same again and again, only changing text, probably it is not important at all.