There are several methods possible.
You could use the Envelope Deformation path effect to distort text which has been converted to paths in Inkscape.
Another possibility is the Lattice Deformation path effect.
These are both available in the Live Path Effects Selector
Both these path effects are quite tricky to apply, so you will have to experiment. They're not perfect. These are also very new features in Inkscape, so hopefully the Inkscape devs will be able in time to improve their usability.
If after making the transformations there are still some wonky lines that you'd like to fix, you can do Path > Object to Path to remove the effects, then edit the paths manually.
There was at one time a Bézier Envelope extension. Unfortunately the extension doesn't work in Inkscape 1.0 as far as I know, at least I couldn't get it to work. I even tried to get this to work with 0.92, but no joy. Maybe install Inscape 0.48 and try it out. The extension is here. There's a good tutorial for using this extension on youtube here.
If you have access to Adobe Illustrator, it also has an Envelope Mesh feature which is a little easier to use. Although again still not perfect, and also can be quite tricky to use.