Is it feasible to create a new language by adding features to C
just as was done with C++?
It's not worth it. The value of C is in compatibility, availability of compilers, and familiarity.
As soon as you change anything in a breaking way, start requiring your own compiler/transpiler, or introduce new idioms, you end up losing the things that keep C alive.
Users of C either like it exactly the way it is, or have to use a specific C version due to a vendor dependency or compliance.
An upgraded C not approved by the standards body gives you yet another niche language that is not C, but is still burdened with its old flaws.
And Objective-C, yet somehow people reinvent them badly in C.
C3 might be it because C3 has full C ABI compatibility so unlike most modern C-like alternatives, it checks out.
There are already plenty of such languages, Zig among others.
I am working on a language that was C with extensions, transpiled to plain C, but the C syntax is kinda not great to work with (stuff like needing type tables and unbounded lookahead). At the point you clean up the syntax, you're not really C with extensions anymore.