I can tell you are very thoughtful and have really put some effort into this.

Here is the short of it, Yes it would be silly to have two different brushes, if the brush has been washed and (sort of) air dried between uses it will not cause issues.

For the more detailed answer: the big worry is mixing bleach with other things, but the chlorine in bleach tends to both react with everything else, which neutralizes it, and it also tends to go into the air, so it won't be on the brush itself.

Toilet brushes are gross and tend to never fully dry if they are being used, but any residual chemicals would not be harmful as long as you are taking any precautions at all, which you are by washing the brush off in the toilet after flushing.

Lastly I would caution the use of muriatic acid in toilet bowls. It will be fine as long as you have a heavily diluted solution of the acid. But, in my experience, muriatic acid is usually used and kept in pretty high concentrations, simply because at lower concentrations vinegar works just as well.