Question: I want the ability to animate a scene where I can draw boxes, circles, text, and other things like images, and be able to record it. I figure I will need my own recording software, but that is separate from this post.

Because my needs are very simple, the tool I use should be free.

Since some of the things will be computer science and math related, originally I was looking at 3Blue1Brown's videos, but the application used for those videos is a bit overkill for what I need.

Answer: 
Modern standard web technologies seem to be reasonably powerful to reproduce what you once did with Flash Player. What about <https://rive.app/> for example?
The excellent OpenFL library <https://www.openfl.org/> uses many of the same APIs as Actionscript 3.0; even the Haxe programming language used in OpenFL is quite similar in syntax/grammar to Actionscript 3.0. OpenFL is made with portability in mind, so native and HTML5 build targets are available out of the box.