Oh, I feel for you - it's a really horrible condition. I'm afraid both oestrogen & progesterone can cause or contribute to constipation in susceptible women. Progesterone has long been considered a culprit, as it's a smooth muscle relaxant that's said to inhibit peristalsis, reducing the strength of the contractions that move food through the gut. More recently it's been recognised that oestrogen can also have an adverse effect, though confusingly some articles say the drop in serotonin that can occur as oestrogen levels decline can also slow the gut. I think it must depend on individual tendencies.
I'm a daily prune/fig girl too, along with all manner of other measures
& sounds like you know what those are, but maybe have a look at the longstanding "Poo!" thread if you have time & need new ideas. Quick suggestions in case you haven't already tried these - a Squatty Potty (horrible name, great product!) can make a big difference, some women find ground linseeds a great help, but just be aware that the lignans in them may interfere with oestrogen uptake & I do find they make flushes & night sweats worse. Some like chia seed though I don't find it very effective. Some take magnesium. Some find kiwi fruit especially helpful. Probiotics might be worth a try, if you don't have an autoimmune condition they might stir up. I've used Proven, Biocare (same manufacturer) & Optibac over the years. One I found particularly helpful is Quest's L Plantarum, from Bodykind online. I also eat natural yoghurt every day, but you'll know that dairy can be problematic for some people & yoghurt's high in histamine. Oh - whole rye bread can be more effective than wheat, if you're not GF.
If upping fibre, fluid, exercise & relaxation (if poss) don't help & this is a change to your gut function on a regimen you formerly had no probs with, then please flag it up with your GP. Not sure from your post whether it's the HRT combination that's new or you're simply having a new trial of a regimen you tried in the past, but if new to you & the problem persists, it could be that you'll need to change the oestrogen dose or the method/type of progestogen.
Another thought is perhaps pelvic floor dysfunction, as that can badly affect the mechanics of emptying. Something to look into if you feel this might be behind it.
Also, though it's important to the body in many ways, Vit D supplements can unfortunately be constipating for some people, especially at higher doses. Ditto calcium supplements.
I hope you manage to get it sorted, as it can feel terrible.
Wx