Has anybody ever heard any of these? What was the sound quality like compared to a 45? Was it really bad?

There were no such things.

There were at least 20, maybe 30 of them. If they didn't exist I wouldn't have asked would I?

EDIT: I just checked - there were 30 in all.

There were! The majority were pressed in India. When Parlophone stopped producing 78's in 1963 the pressing equipment was sent to India where 78's were still in demand as they could be played on wind-up phonographs that didn't require electricity, which at that time many Indians did not have. They were issued alongside the regular 45's from 1964 until 1968 and, as the op correctly states, some thirty singles were issued.

Additionally a 78 of Twist And Shout/I Saw Her Standing There was issued in Argentina. The latter track was also issued on 78 in Colombia, coupled with Don't Bother Me, whilst a second Colombian release coupled I Should Have Known Better with A Hard Days Night.

On the odd occasions when these records come up for sale you can expect to pay four figure sums for them.

There are some videos of the 78s being played on YouTube but they are blocked here by the copyright holders. You could probably watch them if you had a way to fool YouTube into thinking you weren't in the UK.

Some 78s can sound good if played on specialist equipment, again there are YouTube videos of some old recordings that sound remarkably clear. But i doubt the Beatles sound as good on 78 as they do on 45 or 33.

I don't think there was every anything wrong with the sound quality of 78s as such. We only think of them as rubbish now because most of those that survived were very heavily played on very cheap needles, and so have usually suffered a lot of damage. Additionally, some record companies were notorious for using very cheap, low grade materials to make them, and of course lots were pressed during the Depression, the WWII etc.

But in principle there's no reason why they shouldn't sound as good as any other medium. Certainly most modern reissues of records from the 20s and 30s don't sound bad at all.

And just found this...

https://www.youtube.com/watch?v=bWQUauv0i68

....these were actually bootleg recordings made in eastern Europe at the time of Communism using a flexidisk system based on old x-ray film!!!

Back in the USSR was indeed very popular....

When the discs were new and assuming they were played on good equipment, they would sound similar to a 45 of that era many of which were not too hot either. Once played on a heavy pickup, especially one with a steel needle, the surface noise would increase dramatically.

When 45s first came out they played poorly some equipment because the cartridge output was much lower and turning up the volume exposed hum and hiss from the crude electronics. Playing weights were often too high causing the discs to deteriorate, ex juke box 45s were often greyish due to excessive wear, they also hissed and crackled for the same reason. The big problem with 78s was their size and the fact that being shellac they broke very easily. Early ones, pre 1950, had an abrasive in the mix to wear down steel needle to the right profile, this caused lots of surface noise as well. No idea if the indian ones had this.

Flexy discs were often given away in magazines here in the 60s, the quality was usually poor.