Hmm yeah I can see the appeal of something like that. I just had a look in my local Amazon and saw this study timer with a nice physical button which seems to have "Count up" functionality [1][2]. But it doesn't seem to have a feature to alert you while counting up.

[1] https://www.amazon.co.jp/-/en/dretec-T-580WTDI-Study-Timer-S...

[2] https://youtu.be/Ak_TjtWc8uo?t=294 (enable caption)