core::arch::wasm32::memory_size function will give you the memory size in 64KiB pages.
Heap size is a bit more involved, I don’t think there is an API that gives you that directly.
You can get the size of currently allocated objects by defining a custom global allocator that keeps track of allocations, std::alloc::System docs provide an example.
If you serialize/deserialize the whole state on upgrade, this can actually make things worse: Motoko canister memory size increased after upgrade - #6 by roman-kashitsyn
In Rust, Candid encoding for serde_bytes::ByteBuf is much more efficient compared to Vec<u8>.
In case of Vec<u8>, the encoder treats the data as a generic array, encoding each byte as a separate value, one at a time. Same inefficiency affects on the decoding side.
In case of ByteBuf, the encoder records the blob size and then memcopies the contents into the output buffer. This is much more efficient (I observed 3x-10x reduction in cycle consumption for large byte arrays). Note that this is not just Candid issue, the same is true for any serde backend.
I assume that Motoko implementation has similar peculiarities when it comes to Blob vs [Nat8], but I’m not 100% sure.