web-component VS mathlive

Here a few: - Web Component Framework

It does have Vue component, see https://github.com/arnog/mathlive/tree/master/examples/vue

Up until this time, EngineeringPaper.xyz has been using the MathQuill math editor component. This editor worked well but is no longer being actively developed and has some limitations that have limited what features can be implemented in EngineeringPaper.xyz. Specifically, MathQuill does not support vectors and matrices. To enable the future advancement of EngineeringPaper.xyz, the math editor has been updated to use the MathLive math editing component. MathLive is under active development and supports many advanced math constructs, such as vectors and matrices. You will notice differences in how the equations look in your existing sheets. In general, MathLive uses a more modern font set and renders equations more clearly. We have aimed to keep the editing experience as close to the same as possible. One change is the shortcut for the square root symbol. Simply type "sqrt(" to create the square root symbol. Alternatively, you can use the onscreen keyboard to insert a square root symbol.

If you find other problems, feel free to file them here: https://github.com/arnog/mathlive/issues

Maybe you could consider having an editable mathfield so the result can be easily tweaked if needed. I'd recommend https://cortexjs.io/mathlive/ but I'm biased, I'm the author of that library :)