Do you find that after you've prioritized recovery within the next 24 hours, your HRV is back to normal typically? If it isn't do you continue your recovery the day after etc?
Digging deeper into recovery - do you do nothing, or do active recovery like walking, mobility etc.?
Yes, it usually normalizes in a day but not always. I use Elite HRV which gives a score and indicates whether you are sympathetic dominant (S) or parasympathetic dominant (P) when you are out of balance. Balanced is a score of 10 and you're good to go. 7, 8, or 9 S is pretty normal too, and I'm fine to train on these days. After a hard training day I might get a 6S or 7S (4 or 5 if heavy deadlifts the day before, or a lot of volume). If I get less than 6 hours sleep I might be a 5S regardless of what my training was. Hard training day plus not good sleep plus other life stress and it might be a 3 or 4 S. Following it up with non-stressful day and a good night's sleep will usually right this the next day.
P scores are a little more odd. It's more like the body is in deep recovery mode. If it's from getting an extra good or extra long night's sleep, it's a good sign and will usually be normalized in a day. If it's from recovering from a long stress (too many S days in a row, or too many days of hard training in a row, or being sick for a week or so) then I might see several days or a week of of P. I should be more cautious on these days but I'm not always. Rarely do I let the HRV talk me out of what I plan to do in training. I just take it into advisement for the day as a whole.
To recover from being overly "S" I might actively try to relax during the day and focus on breathing, and try to eat well and get a good night's sleep. I feel like a reduction of sympathetic dominance is usually a good thing to seek -- basically it's reducing your body's stress response, which mostly tends to be too high. I might try to make my training less stressful (longer rests, etc.).
I don't necessarily try to get myself out of "P" because I usually feel like my body is doing what it needs to do. I just work with it... usually I feel pretty good on these days, just not energetic or ready to lift heavy. Also not as focused at work or elsewhere. "P" tends to make me kind of dreamy and unfocused, but in a pleasant way. Mobility, stretching, and movement practice are great on "P" days. I've noticed that I get great feedback from the body on these days so I can do some light or slow practice of a movement and really learn a lot.