So main issue is in the subject line although I notice when I go to Config->DVB Inputs->Services and click on a channel's "i" button, it displays no subtitle stream.
HOWEVER, when I do direct stream profile (e.g. default "pass" profile) I get closed captions. I did see various screenshots of the info page and I know it should list them there. The main objective is to keep the subtitles of recordings and record in h.265_vaapi (that part works really well)
System info:
HDHomeRun Connect Quadro (setup as "TV adapters, I saw some videos suggesting setting them up as IPTV, not sure if needed)
HTS Tvheadend 4.3-2008~ge2ae8f4eb
Newish i7 machine