I do it on an rpi3 HAOS and external hdd, very rarely. The rpi3 is down at my parents. It doesn’t really run anything else. I basically setup HA for remote access to the rpi3(which is handy for doing updates and things).
To be clear it only streams when we visit my parents, and even then usually only 1 stream via chromecast. I set it that up to watch the videos on the HDD when we visit and for my parents to play music. They never really took to casting music to the tv via chromecast.
I use HA Add-ons by alexbelgium - emby instead of plex. Just my preference. I had originally meant to set it up at home here, but I got an rpi4 instead. My computer that my emby server at home is on, disconnects when it goes to sleep and wake on lan never worked on that motherboard. So I had meant to set up emby on the rpi4, but never got around to it really. We just cast netflix or whatever, and on the odd occasion we cast emby, it is easy enough to wake the computer up manually.
On the rpi3,I have extended
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extended the swap memory to 2gb no idea how safe that is for ther SD card, but its still sitting there a year or so later.
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setup SSL for emby to cast to chromecast. It runs two domains, one for emby and one for HA using duckdns and nginx proxy manager.
It works the rpi3 pretty hard when streaming. I doubt it would cope with two streams. So doable… but your expectations need to be low.
edit:
It is sitting around @ 70% mem use and 3% processor use atm. I was setting up remote home-assistant when I saw your post.
It didn’t like that very much went up to about 75% processor use.