It'd be a neat trick to have a single unified language which could bridge the gap between software and hardware description languages.

The hardware description languages, even if they have a single language specification, are divided into 2 distinct subsets, one used for synthesis, i.e. for hardware design, and one used for simulation, i.e. for hardware verification.

The subset required for hardware synthesis/design, cannot be unified completely with a programming language, because it needs a different semantics, though the syntax can be made somewhat similar, as with VHDL that was derived from Ada, while Verilog was derived from C. However, the subset used for simulation/verification, outside the proper hardware blocks, can be pretty much identical with a programming language.

So in principle one could have a pair of harmonized languages, one a more or less typical programming language used for verification and a dedicated hardware description language used only for synthesis.

The current state is not too far from this, because many simulators have interfaces between HDLs and some programming languages, so you can do much verification work in something like C++, instead of SystemVerilog or VHDL. For instance, using C++ for all verification tasks is possible when using Verilator to simulate the hardware blocks.

I am not aware of any simulator that would allow synthesis in VHDL coupled with writing test benches in Ada, which are a better fit than VHDL with C++, but it could be done.

It's an intriguing idea. Having experience with software but almost none (only hobbyist) in hardware, I imagine it'd require a strong type system and mathematical foundation. Perhaps something like Agda, a language that is a proof assistant and theorem prover, with which one can write executable programs. https://en.wikipedia.org/wiki/Agda_(programming_language)