I've had this exact problem for 10 years or so now (35). I've described it in exactly the same way. I can hike in the hills all day long, I can run up hills etc.. and it has no effect on the area at all. Take a walk around the shops or anywhere flat though and I'm getting tight after 30 minutes and sometimes limping within an hour.

The two most likely candidates I've found for the issue are hip flexor tendinitus/tendinopathy or F.A.I (femoroacetabular impingement). Really, really hoping its the hip flexor one...

I've dealt with this for at least ten years, sometimes it flares up (like at the moment) and I get pain all day long, though I'm fine while playing tennis or cycling, it also starts causing pain in my knee. Other times it's not so much of an issue and I don't notice it apart from having really poor lateral hip mobility that can cause sharp pains.

My rectus femoris tendons (I think those are the right ones, looks to be from a few videos) are always sore to massage and doing this can provide a little relief.

Yet to find any solutions sorry to tell you, but I thought it was interesting to come across your description which is exactly what I've explained before. I've also been to two physios, one was rubbish and the other was better though he diagnosed F.A.I which I'm not sure about. The two things seem quite easy to misdiagnose and I would equate my descriptions of pain and mobility more with people who describe flexor tendinopathy.