I'm not sure what I want for an STM32 micro
They have a number of application notes, such as
https://www.sitime.com/support/resource-library/application-notes/an10037-optimized-sit15xx-drive-settings-32-khz-inputsLooking at the MEMS you linked to it says a stability of 75ppm over a more or less commercial temperature range. That isn't good enough for USB either.
How can <100ppm not be good enough when full speed requires +/-0.25% (2500ppm). Even the high speed requirement is above 100ppm (+/-0.05%, 500ppm).
Your problem in getting an internal clock trimmed for usb is most likely not the LSE reference clock, but how well the internal clock can be trimmed. If the internal clock moves 0.5% (5000ppm) for each trim value increment/decrement, then the resolution of trimming becomes kind of coarse for the job.
In practice, I think usb is more tolerant of the (low/full speed) clock than the design requirements, which have to take into account some max number of hubs in a chain, and so on. I had a pic24, which to use the internal clock it had to be routed externally back to the external clock input so it could drive the usb clock (via pll). The SOF was used to trim the internal clock, which worked ok, but manually trimming the internal clock to its max values while testing never resulted in 'losing' the usb functionality either (don't remember what the actual usb clock freqs were, but were quite a bit outside the allowed range at max trim values). This was at normal temperatures, and I am simply pointing out that usb doesn't quit working when you reach the specified tolerance threshold.
I take it you do not want an external crystal for the main clock, but you are trading that problem for a different one (an external low speed clock + code to do trimming). There are also crystal-less mcu's in the stm32 family which are also an option. I would assume one could also do something on your own like I did on the pic24 and use the SOF to trim the internal clock. The best option is probably to just let hardware deal with this- either get a main clock crystal or get a crystal-less mcu.