Ollix!
It's ALL about the engine.
I used a rigid hybrid for many years. Did forum rides, sportives, etc and never found myself lacking. Would still be using it now if the frame hadn't cracked.
Still 'smash' many other riders on 'performance' bikes when riding my current commuter bike with loaded panniers and mudguards.
Just returned from Spain and after one particularly hilly ride I encountered a young Spanish racing snake. I had ridden about 80 miles in mountainous terrain (altitudes over 4000ft) and he chatted with me about chain ganging back into Girona because of an unfavorable headwind. We set off with him on a skeletal road bike and me on a sub-optimal gravel bike with twiddly gearing. After 10 miles we hit a bit of a climb and I suddenly looked round to find him dropped off the back and disappearing fast. I did the final 15 miles alone
. Probably 25yrs his senior but still had the legs to ride away from him despite the miles, climbing and bike choices.
What is your current bike? I would suggest not changing bikes at this stage because you risk making things worse. There are many minor changes that can be made to optimise your current set up before you think about changing bikes.
I'm going to disagree with you now - while the engine is the most important, obviously, the bike can and does make a difference.
Forget about you vs a weaker engine since that is a disingenuous way to try and prove a point on this subject and focus purely upon you vs you.
On a tarmac road, you would be faster on a 7kg aero racing bike than on your hybrid or commuter pannier bike. This isn't marketing BS, it's fact.
You doing a constant 200watts would be faster on an 8kg road bike with 28mm tyres than a 9.5kg 29er MTB with 48mm tyres on tarmac. You know this to be true so to say that it is "ALL about the engine" makes no sense. The bike will have a very significant effect upon how fast you ride.
At 54 I regularly beat cyclists younger than me too but faced with a cyclist my equal in watts/kg, power and fitness etc then the bike that saves the most watts on a given route is going to have a significant impact upon the results of a race.
I've performed countless tests using Strava segments on my various bikes. Most recently I tried to get a few road KOM's on my new gravel bike; I got one but couldn't get another couple I was aiming for. When I switched to my Summer road bike, I got them. On a closer scale, I have done the same with all 3 of my road bikes pitting them against each other on the same segments. I've done free-wheeling tests with friends downhill. Brake tests. You name it, we've done all the GCN+ stuff for fun ourselves. It isn't marketing BS...aero and lightweight tech does make a difference.
Saving watts is the main goal of higher end road bikes. It's true, however, that those potential savings in energy come at an increasingly higher price as you go up the tiers to the point that they are very expensive for very marginal gains.
We choose how much we are prepared to invest to get those gains and if we find we are quite happy riding our hybrids and commuter bikes and still able to overtake weaker engines on more expensive bikes, great! All that means it our engines are that much stronger than theirs.
But make no mistake, we are faster on bikes that need fewer watts to cut through the air or haul up an incline.
To the OP, find a bike like the Trek shown above, strip it down, clean it up, get it running smoothly and it'll be fine for your ride. Don't push yourself, enjoy it, take in lots of fluids, food.