With a Wear OS watch you can record the match for real: how many shots you hit, how they split across sets, the rhythm you played at and your heart rate. You turn it on per match and you decide.
With the match open on your phone, go to the ⋮ menu and tap Record shots and heart rate. It explains what gets recorded and who sees what. You only do this once: it stays on for your next matches.
This is the one people forget: the watch measures from the arm holding the racket. If you normally wear it on the other one, switch it before you start — on the non-hitting arm nothing is detected.
The first time, the watch asks for heart rate and for showing notifications. Both are needed. If you decline heart rate, the match still records, just without it.
Recording starts by itself when the server is declared, not before: that way the warm-up doesn't count as the match. You'll see a notice on the watch: 'Recording shots', with minutes, shots and your heart rate.
You can switch the screen off and pocket the phone. The watch keeps recording on its own. When the match ends it stops and sends the report.
On the finished match, tap the racket icon. There you'll find your shots, how they split across sets, your rhythm in shots per minute and the match's heart rate.
If several of you wear a watch, each one records their own match. Each just needs to open the match on their own phone. Afterwards you can compare shots and rhythm.
Shots and rhythm are seen by all four, because they belong to the match you played together. Only you see your heart rate, and not because the screen hides it: it lives apart and the server hands it to nobody else.
Today it works with Wear OS watches. Apple Watch can't record shots or heart rate yet. Shot type (smash, lob, volley) isn't told apart: we'd rather give no number than a wrong one.