Are there any benefits of using Library and 64-bit version?

My habit, when i get new files: about 20-30 times (yes!) to save changes, before new files will "all right" for my phonoteca. Because i use a lot of tags (30-40 or more), they all have to be searched for, typed in -- and always saved.

You are quite right: this topic has been discussed several times.
And I still wait for the real use case.
With the use of the library that helps to load your whole collection in just 2 minutes, you have all the template files at hand they you may ever need.
And for more specialized cases you have the quick actions, action groups and/or converters.

which means that the real time lag comes from the search and the time it takes to write the tag data to the files can be neglected.

I tried it thoroughly, when the Library came out. I do searches in foobar, writes in Mp3tag. So this is the fastest way for me, i tested it.

I wrote above:

About once a month.

For me, the Library would be worth, if there were those drop-down lists, based on it. Then it would be faster, than always to jump to the foobar. Which, by the way, is not so common way in my practice. What i need to copy, i open (most of them) in Mp3tag. I use a lot of export + import, for example like i described here: Data in REAL database, instead of tags?
Often, I modify the exported aaa.txt file in EditPad (or Pro) first (also a great program), before importing it into the new files.

This may be important. I saw a very OFTEN reads-writes. Does this mean, that the Library file has been modified, saved on disk so many times? Because if so, it might be more appropriate to save it only once, at the very end. (Sorry for the perhaps amateur post.)

I doubt that.
How many artists does foobar show you? They all would appear in the dropdown list I would assume - or, if it can be maintained by the user, you would have to remove the unused / unnecessary one-hit-wonders from the list.
Or you scroll endlessly through the dropdown list ("Was it 'Beatles' at 'B' or 'The Beatles' at 'T'?").
So I still think that a dedicated set of actions of the type "Format value" is the fastest way.

The library, BTW, was never intended for external access and purposes. Even the shorter loading time is just a welcome by-product but not an intended feature.

Good databases are random access databases where the sequence of records does not match a particular alphabetic order. Data is usually accessed via an index mechanism which helps to find the record position in the database.
So the reads and writes mean that the database handler made the pointer jump to a specific position and read the data from there.
New data can simply be appended at the end without the need to rewrite the whole database file.
Deleted records are simply flagged as deleted and not physically removed from the database. You have to trigger such grooming in Tools>Options>Library.

Agree totally, again.

Artist: i have actually 4,000. But, imagine the really perfect solution: type "t". For 3 sec delay nothing happens. This delay must be (even adjustable by the user)! I instantly continue with "les." And i get the Beatles, and everything where "tles" (full-text search!) occurs. I only have one thing left: to click on the line, that is right for me in the list. And the task is done.

I know, there is a huge resource requirement. But even more powerful help at work.

You wrote: if it can be maintained by the user, you would have to remove the unused / unnecessary one-hit-wonders from the list -- i am completely opposed to this, manual variant.

Thank you, @ohrenkino, for really useful explanation. I did not know it yet.