I'll spare you my rant on why I don't like InfluxDB lol.

In the end it depends how much data you're dealing with. If you're only ingesting dozens to hundreds of records per second per writer you might actually like AWS Time stream. If you're dealing with a million + rows per second from a low number of writers (e.g. scientific data) then you probably want Influx or Timescale. If you want to host it yourself and you have less than 1TB of data then Influx is okay or if you want it cloud hosted then Influx may be a good option.

If you need full control, scalable, TB or PB of data, etc. Then Timescale is great but it's definitely more work.