dbgsym package contains debug symbols.
Ignore the dbgsym package
If your program (mysql in this case) is written in a compiled language such as C, C++, Go, Rust, etc and converted into an executable then debug information allows a certain amount of referencing locations and values from the executable back to the original source code.
For example it can say that bytes 300 through 312 and 340 through 356 came from line 127 of file src/main.c.
Also it can say that the variable foo is stored in register %r12 when the program counter is between 500 and 512.
If the program crashes, perhaps due to doing a divide by zero, then being able to say that you were executing a particular source code line and using a particular variable can make things much simpler to get a fix.
However all of this information takes space. As most people are not going to want to debug programs such as mysql, distributions frequently split the debug information out into an additional package so that people who are not interested don't pay the costs of downloading and storing it.