You seem to be asking two questions here: What was the popular regard for historically great musicians? What regard were they held in among other musicians?

Luckily there are answers to both. I’ll stick with the three you named and if you want more follow-up I’ll dig into my books.

Popularity amongst the public

This is slightly more challenging because surviving critical accounts come from critics who were often musicians themselves and thus get into the territory of the second half of this.

Nonetheless, we know that Bach was renowned as an organ virtuoso, but was also hamstrung by his employments - though even this points to his interaction with the public and not just royalty. His contract in Leipzig required him to be an exemplary member of the town, beholden to the town council, and he was unable to leave without permission of the mayor.

Records tell us that Beethoven’s music was immediately popular and hasn’t fallen from cultural consciousness since. He was able to live solely on the publication of his music and support from patrons even after his hearing impairment forced him to stop performing. When he died, ten to twenty thousand people came to his funeral.

Mozart’s star certainly rose as the result of his touring. While he had issues with wealth or immediate fame in his adult life, much of this wasn’t due to his terrible management of household finances. His operas were consistently successful and at the time this genre was the most prestigious. Still, the complexity with which he wrote did hurt him some at the time (and I have quotes below about this).

Popularity amongst peers

This is easy to answer because we know a lot about who learned from whom and who was inspired by whom.

Bach, for example, had a strong fascination with Vivaldi when he was in Weimar in 1708 and did arrangements/reorchestrations of existing Vivaldi works. This brought about fundamental changes to his style. Here we see Bach himself taking great inspiration from another composer.

Hayden taught both Mozart and Beethoven. Of the former, Hayden said to Leopold (Wolfgang’s father), “I tell you that your son is the greatest composer known to me either in person or by name.” Some composers, though, felt that the complexity of his music put it beyond the grasp of contemporary audiences. A minor composer named Dittersdorf, speaking of some of Mozart’s quartets, said that while they “deserved the highest praise,” their “overwhelming and unrelenting artfulness” turned off the public at large.

I mentioned Beethoven’s position in the cultural consciousness earlier and this was certainly true among his peers. Later composers used him as a model, some putting him on quite a pedestal. Bruckner, for example, was nervous about his own ninth symphony because it was in the same key as Beethoven’s Ninth.

I hope these examples are helpful in the ways you were hoping for. It may be interesting to know that there are similar accounts available for composers that are lesser known today. Renaissance musician Josquin does Prez, for example, was essentially a rock star amongst both public and peers, with a healthy catalogue of sacred and secular music (El Grillo being a favorite of mine).

Later composers were as much critic as composer. It may be worth looking at Berlioz’s writing for examples of that. Schumann also wrote many critiques, primarily in the periodical “Neue Zeitschrift für Musik”. Sometimes, through these critiques, you can find an interesting war of words between musicians who prefer different styles.

Apologies for any typos, I’m on mobile and may have missed some corrections that I fatfingered. I’ll clean this up a touch when I’m on my desktop.

Sources:
Burkhokder, Grout, Palisca - “A History of Western Music”
Bonds - “A History of Music in Western Culture”