Well, even if Jitsi doesn't have Push-to-Talk, you can still easily get it by using a hotkey to mute/unmute the mic system-wide.

For exampple, if you're on PC, MicMute [1] can be used for free, or if you want more customization, I would humbly present my side project, AutoPTT [2].

[1] https://github.com/SaifAqqad/AHK_MicMute/

[2] https://autoptt.com/