why do I have huge log files (SQLFT000060005.LOG.x, 3+Gb) with recent timestamps when I haven't used SSMS for 4 months? ...plus several ERRORLOG.x files ranging from 200MB to 2.1GB ... 

I installed SQL Server 2017 in January for an assignment, but haven't used it since then.
Now the logs files are hogging 22.8GB of space, with recent datestamps - how is that possible?
What can I do to remove them - just delete them?
Log files are created by the SQL Server service, not by SSMS. If you installed with the default settings, you can stop and restart the service multiple times (or just call sp_cycle_errorlog repeatedly), and that should cycle away the big log files that are there. They'll come back, though, over time - even if you don't open SSMS.

If you don't need SQL Server to be running anymore, disable the service or, if you don't need it at all, uninstall it. You can also uninstall full-text search if you aren't using it (or never needed it). Those FT logs might be from that service.