Could Mobilizon be used for that?

EDIT: for finding a date for some other thing I've been happy with how Polls in Nextcloud work. But NC might be too big for your needs. Maybe something from those would fit you?
https://github.com/manfredsteger/polly
https://awesome-selfhosted.net/tags/polls-and-events.html

I don't run games but I would use https://lettucemeet.com/ to poll availability depending on system and one-shot or campaign.

Fall back on discord for communication once you have a group to hammer out location and finer details.

Sounds similar to running a West Marches style games. Pool of GMs and Players.

It's the thing where local forum win

-can be read by non member

-are local focused

-Easy to run/manage

A pitty that they have been replaced by meet up/Facebook ( and their fcdi alternative)

You can use Google Forms to get the RSVP functionality you're looking for. And maybe a dedicated Discord channel with suitable posting restrictions so it's JUST DMs posting such forms? Or you could even have them DM you their pitches and you post them, such that you can make the channel so only you can post. I also like using this tool for scheduling: https://www.when2meet.com/

I don't know of a platform that specifically caters for this. Would be interested to see what others suggest. I've found opportunities locally at game stores, Discord, through meetup, and also through Reddit (apologies Lemmy but there is not enough user base for a city based ttrpg comm here).

Meetups is good if you run a regular session and are open to drop ins Discord and Reddit or some forum styled website would be better to fish for interest in something, but people's schedules and priorities change so you will have to ask regularly. Not much you can do about this. I don't see this as the platform's fault, rather the nature of what you are trying to coordinate.

If discord messages fading too quickly is an issue you can create channels for the different games you are trying to run, or give each GM their own channel for whatever they're pitching, and pin a message in each so they don't get buried into oblivion. I have joined servers that use this system, not for ttrpg admittedly, but this functionality solves that issue.