You are outlining two very different issues & use cases here:
- This outside riding use case (flat vs climb) has been covered in the forum and bouyed by a great CT article (RIP old CT).
- RPE & Power on climbs vs flats
- https://cyclingtips.com/2013/09/climbing-and-time-trialling-how-power-outputs-are-affected/
- Wattage on flats vs climbs
- I am going to leave this at those posts above because they cover that outside use case well.
- This relates to bike fit and rider position on the bike. Your particular change is most likely about the changes in your upper to lower body position and it’s impact on the power production from your entire body. Changes in the relative “hip angle” between simple changes of riding on the tops, hoods and drops of a road bike can all impact how it feels to produce identical power.
Without a before/after picture, it’s not possible to know for sure what you are doing when you alter the bike pitch angle.
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If you stay “stiff” and your entire body just rotates rearward along with the bike, there is effectively no change to the body angles or power production demand on your body. There is a pure alteration with respect to gravity and the forces you exert on the contact points, mainly the saddle and handlebars. This can lead to a better feel for many for the reason that Power13 mentions. I have long advocated for a higher front axle on indoor setups to offset for the loss of the rearward push once we remove wind resistance from outside. A higher pitch takes a bit of load off the hands and shifts it to our bottom, much like wind resistance.
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If you are “flexible” and actually have your upper body “stationary” or rolled more forward as a result of your lower body pitching rearward, you are altering your hip angle on the bike. It’s akin to riding a bike flat and moving down from hoods to drops, or even just bending your elbows to rotate your back and hips forward. This all closes the hip angle and can impact the loading on each muscle group. Doing this at a minimum may shift the load enough to feel like a “relief” to those loaded muscles. Additionally, it may place you into a more “optimal” alignment for power production that is efficient and feels "easier.
Ultimately it may well be a blend of those, but that is the basic summary of the dynamics that might be at play here.