Alternative to Sky Q - compatible with projector?

I'm looking into possibly moving from SkyQ - we've had it for a very long time now, so the price has got stupid, particularly seeing as we watch a lot of streaming that isn't included.

What we currently have:

• SkyQ, with netflix included. No sports/cinema
• NowTV for Sports/Sports Extra. We use the tv for this sometimes, but for big matches/F1 races we switch to a projector.
• One multiroom box that has never been particularly great - always loses signal despite a signal expander and other devices working fine in that room
• Disney+ subscription, Prime subscription (Netflix and discovery+ included with sky package)
• We don't watch a lot of terrestrial tv - although there are a few programmes occasionally on Channel 4 or BBC that we record and watch back. Husband watches a lot of history channel/discovery stuff, I watch random stuff on the streaming services mostly, with an occasional series recorded from terrestrial tv and watched back. Teens only use streaming stuff other than when they are watching sport with us.

What we need:

• Compatibility with projector. Apparently SkyQ doesn't allow it. The projector has usb/usbc and micro hdmi connectors. At the moment we use various apps on it (NowTV, RTE player etc), but would be good to be able to just plug in the TV for matches on RTE etc.
• Sport. Lots of sport. Happy to keep going with NowTV if necessary - although my youngest tells me that there isn't enough F1 content there (apparently sky sports when you get it direct allows for multi-viewing of drivers during the race which is very important to her)
• Recording ability - happy to go through players/apps if necessary
• Plug and play. I don't want anything that means switching between boxes, fiddling with settings. I don't have the time and energy.
• Multiroom of some sort. Even better if it can move easily between rooms. The Sky one seems to require a complete new set-up every time it gets disconnected from the tv.

Are the eir/vodafone/sky stream options pretty much equal for most of this? And then it's just a case of price? Virgin isn't an option where we are. The projector compatibility is the big thing really.