Best way I can think of to promote carpooling is kind of what colruyt tried.

Employee bus that goes down the main highway ( Belgium ). It has WiFi and you csn keep working on your way home. Every minute worked counts.

You'll just need a bigger carpark by the highway. 30 minutes delay? It's not lost time. Still want to use your car? Sure. But you'll work longer and have to drive home afterwards.

I am not a traffic expert. The approach might be flawed. But it seems like a step in the right direction.

At least it's better than complaining about overcrowded busses and trains who are delayed again. And while it might not solve the issue, If you can get a 10 people per bus. It should start adding up eventually. The incentive to take public transport doesn't disappear with the disappearance of traffic jams. Its an alternative to sitting longer in the office and being home later.

I think colruyt did something like this for a while? https://reset.vlaanderen/2017/09/01/kantoorbus/

Maybe its something you can book a seat on and should be scheduled on a larger scale than just 1 company.

One can dream I suppose. Hell will freeze over when most companies will "trust" their employees enough to work on the bus though.