Upgrade to mirrorless??? EOS R5C

[echase]

Hello!  I'm looking for some help.  I trying to decide if I should upgrade to a mirrorless camera or stay with the old DSL that I have.  A little background, I'm a novice at best, I have a EOS 60D DSL that is about 13-15 years old.  I have been wanting a EF 70-200 f2.8 lens for years and have never bought one.  My kids are in sports and musical competitions and now I'm finally ready but as I started to do some looking I noticed that things seem to be moving to mirrorless.  I looked at the EOS R5C and a 70-200 lens and it's a pretty penny.  My only real goal is to get good pictures of my kids up close as I move around the field and concert venues.  Could I get video with this camera as well? I would also like a fast auto focus so I can get good action shots.  I also don't see myself digging in really deep to become more proficient than what I already know (maybe a little bit more knowledgeable).  

If I buy the EF lens for the 60D am I investing in an old technology?  Would I be better off moving to mirrorless now?

Any help and advice would be appreciated.  

Thank you!

[echase]

Thank you.

[Tronhard]

Hi again:
As I understand it, you are challenged with setting a budget.  Simply put, how much money overall (to cover all items) are you prepared to comfortably prepared to spend on your photography gear?  With that overall value, we can suggest a balance between a body, lens and associated items to try to provide a balance that will work for you.

We cannot provide relevant information that is viable without that one item to start off with.  Just know that you should not put your own finances under strain to do this.