can I use my HomePod mini on my roku tv without having a Apple TV?

I don't believe so. Looking at this article from Roku https://support.roku.com/article/360057488733 it seems some of their devices can act as AirPlay targets, but I cannot find any indication they they can redirect their audio to HomePod.

tt2

few if any devices apart from ios devices and macs and windows using the apple apps really support targeting airplay 2 receivers, I suppose it's a feature that apple would require royalties for other manufacturers to implement.