The TSL actually lets you do a lot - almost anything, really. It's an open source license (I even used little o's!) that is designed to only prevent cloud providers from selling TimescaleDB as a service.
I can't help but wonder if they're using the phrase "open source in spirit" to leech the branding of open source (while ironically treating other companies as leeches).
The established meaning is “any non-F/OSS licenses that nevertheless provides free access to source code, which may or may not also provide some usage rights”
TSL is exactly that.
There might be some utility to a name for a new subcategory of source available, but it's not meaningfully similar to open source since it remains, ultimately, a traditional, rent-protection proprietary license. The fact that current market conditions give a very particular rent-extracting opportunity that the vendor wants to protect and the vendor focussed rent protection where the most value is...is not unusual, even if the exact current valuable rent-extraction opportunity is different than it was even a few years ago.
It doesn't really - it's been used to describe a pretty broad range of licenses. "Source available" means you can read the source but do not have all of the rights you'd get from an open source license. Which is the case for TSL.