If you switch from asciimath to latexmath, you get more control over size.

(You can use site https://www.intmath.com/help/asciimath-input-latex-katex-output.php to convert asciimath into latexmath).

Then you can use \scriptsize (or other sizes listed at https://www.overleaf.com/learn/latex/Font_sizes%2C_families%2C_and_styles)

Or use \scalebox{.7}{text} to scale.

Unfortunately I could find no way to explicitly set the font name and size.

e.g.

@startuml :This is a test with math<latex>\scalebox{.7} {\displaystyle{a}\cdot{x}^{2}+{b}\cdot{x}+{c}}</latex>inside text; :Let the formula: <latex>\scriptsize {{ \int_{{0}}^{{1}}} f{{\left({x}\right)}}{\left.{d}{x}\right.}}</latex>; @enduml

Another example using tt font for 1st, and \tiny for 2nd :

Hello A.,

Here is an example:

Not only the size, there is the alignment...

But the big deal: how to manage big formula?...

Align on bottom, on middle...

To debate...

Regards,

Th.