This is an old version of J_Ott's ShapeKey Helper tools That works in Blender 3.6.5! (The newer updated versions throw errors & I'm no programmer to fix them D:)
Installation: All you'll need to do is drag the shapeKeyHelper_menu.py into your blender addons folder. You'll then see it in your Preferences> Addons > 'Mesh:ShapeKey Helpers
How to use: The shapeKeys Helper menu should be located in the data tab. There you'll be able to press the function you want after selecting the model you'd like to apply the modifiers and keep the shapeKeys.
Known Issues: "ShapeKeys are not transferring fully" If this happens, You have to disable merge and clipping on the mirror modifier. (While having merge and clipping on, blender tends to mess up the verts. The addon is heavily dependent on all verts staying the same.)
Be sure to check out the forum link! You can find the other versions here in case you'd like to try them yourself. https://blenderartists.org/t/addon-shapekey-helpers/1131849
And last here's a link to another ShapeKey tool. https://github.com/smokejohn/SKkeeper
Hope this helps, happy blending!