The F-15 program was accelerated partly because of a fear (and ignorance) of the MiG-25's (Foxbat) capabilities. The 31 (Foxhound) is a newer version of the 25, it appeared years after the Eagle was already a thing.

Were the Soviets intimidated? Well, to a certain degree, sure. The Eagle soon proved to be a very capable fighter, with its first air to air combat in the hands of the Israelis resulting in an overwhelming success.

However, the Soviets were of course already working on their own answer to the Eagle, the project that would eventually result in the Su-27 Flanker was already cracking on. The same project also spawned the MiG-29, much akin to how the USAF ended up with the F-15 and the F-16 (though those didn't originate from the same program, but otoh the F-18 was an off-shoot of the program that spawned the 16).

So the USSR was well aware that the F-15 represented a leap forward (it was one of the first 4th generation fighters after all, if not the first), but they were already busy building their own new toys, so it certainly was not like the Reds were running around the Kremlin panicking as if their hair was on fire.

Of course, the Soviets started their new project when they learned of the USAF's new project, but that's just how arms races go, be it for swords and armour, battleships, high tech jet fighters or really whatever else. I certainly wouldn't want to paint that with an 'intimidation' brush, seeing as intimidation through potential power is basically the driving force behind an arms race in the first place.

To explictly state there was (extra) 'intimidation' involved would suggest something else besides the 'usual arms race stuff'. Like the "Tank Panic" of '41, where the invading Germans were quite surprised at the power of Soviet armour, one could say 'intimidated', and were now rushing to update their own armoured forces. Or like the initial situation which you referenced, when US analysts vastly overestimated the capabilities of the MiG-25 Foxbat, prompting an upscale of the requirements for the next USAF fighter plane.

In case of the F-15, though, the Soviets were aware of the program and they were already countering it.

One thing to remember is that, certainly in the modern age, large militaries are always trying to build the new next best thing. It's not like the MiG-25 "made" the US build F-15s. The next US fighter would've been made regardless of the MiG-25 and the next Soviet fighter would've been made regardless of the F-15. And it's not like you can get an accurate assessment of the opponent's stuff to amend your own design while still in development, it's usually too late for that if it happens at all. Guesswork and estimation is the only thing you can work on, short of actually inspecting a real specimen.

There were indeed occasions where an enemy's weapon prompted an acceleration or amendment to a weapon's program, like the aforementioned 'tank panic', but on the whole I find the "the Red side made X, so the Blue side made Y, then the Reds made Z" trope to be a very simplified and exxagerated version of events, because with hindsight, we are looking at X, Y and Z as finished weapons, when at the time they were usually just stuff in the pipeline.

It's not like "Blyat, the damn Yankees have built F-15 Eagles with massive list of specifications ", but more like "The Yankees are spending a lot of money developing a new airplane, we better do the same". The Eagle isn't intimidating anyone here, billions of dollars on a new weapons project is, long before the Eagle is even an Eagle.

So, to come around to the question, no, the Soviets were not intimidated by the F-15 beyond standard arms race context. They knew it was coming, they knew it most likely be good and they were already building their own new toy.

I doubt little. Sort of a game of numbers, while the West often had good equipment the East had lots of equipment. In the end the main buff a boo remained the same, nuclear weapons. ICMBMs and sub launched.