Last summer I dealt with OTS and it was similar to how you describe it, where the effort felt hard but HR did not increase in similar fashion and resting HR was maybe 2-3 bpm higher than when properly rested. The path into and path out of OTS are likely individual, but for me it was a matter of patience and accepting I dug myself into a bit of a hole (but I can try to lay the blame on raising a second dog for skijoring). Not getting outside was not a realistic/acceptable option, so I did continue to train, but with reduced volume, only easier effort (both in terms of RPE and HR), and no long runs – the total opposite of what would normally describe the summer season. Just as with coming back from an injury, every now and then I would push for a short section just to test how it felt, but never as a sustained effort. In short, it was a patience game.

OTS for me was a combination of same amount of training hours per week (9–12 hours/week) during winter 20/21 but broken up into more smaller bits to accommodate running, training with an adult dog and building up the condition of a puppy – for quite a while it was 30-45 minutes 3 times per day; and reduced sleep quality with a puppy (compounded by our early sunrise in the far north; 3:15 a.m. right now). The transition out of winter 20/21 to bare ground season physically seemed to start well, but the chronic under-recovery from reduced sleep quality I believe was the bigger factor that did me in. Although maybe the specific circumstances were unique, it was essentially classic chronic imbalance between recovery and stress.
More-or-less recovered from OTS now, I believe; the main challenge is still re-calibrating the balance between the bikejoring/skijoring with the 2 dogs and running, but it is working well now. I have avoided longer runs (>2.5 hr) so far and am only just rebuilding that endurance – but think during July I should be back pretty close to a normal solid base and plan on a 100k in August. For that, however, I will not be at 100% race form, so the goal will be to put in a good, but very controlled effort and not go absolutely all in.