Big Home Assistant fan here! And it's made by a Dutch guy :-)
Easiest to run it on a dedicated Linux box somewhere, because it's a bit of a Docker circus.
Discussion
I'm so glad I asked this and can see the wizardry you guys are on. Despite it being gobbledygook to me :)
Glad you're all having fun tho
Also I would recommend to integate with influxdb, for persistence of historical data. Then put grafana on top of that and you can add your grafana graphs into home assistant with the external web page card.
I've just been hoarding 1+ year of sensor data with no plan. Had to get a larger SSD (for other reasons too). This might be a good idea.