To make new proteins, you have to create new ribosomes, as it's they who interpret the RNA codons to stitch amino acids together. Bootstrapping a new ribosome is several magnitudes harder than constructing a synthetic DNA/RNA.
Actually, you don't even need new DNA letter to do that. DNA codons can encode 64 different amino acids (63, as one codon must encode the end of sequence), but only 20 amino acids are actually used.
Adding another amino acid is theoretically possible, but this would require rewriting the whole DNA to reencode, say leucine from CTG to another codon to assign CTG to some other acid.
I don't think you'd need entirely new ribosomes, assuming the new bases are relatively the same size as ATCG. What you'd need more of are aminoacyltransferases, which load amino acids onto tRNAs. You'd also need new tRNA's (probably not super hard), and I imagine you'd want new amino acids. But we don't even know how to predict how existing amino acid chains fold into functional proteins, so I'm not sure what the goal of making new amino acids would further.
More likely, the new bases can be used as a higher-density data storage medium for those folks interested in making biological data stores.
Silicon/Bismuth biochemistry is way more limited than Carbon/Hydrogen Oxide biochemistry in terms of temperature range and stable compounds. Silicon/Hydrogen Sulfide biochemistry does not work at all because hydrogen sulfide does not have the point of least volume.
biochemistries listed here are denoted as bonding atom/solvent pairs.
I think for now we are still a ways off from this being interesting at the protein level. I would think you would need new tRNAs to recognize the new bases in-order to really utilize them at a protein level, and those tRNAs would need to bind to different amino acids than we currently have for there to be any new protein function that we can't already accomplish with ATCG.
That being said, you can still do a lot of interesting stuff with nucleic acids like DNA and RNA, more and more research these days show they can do more than just encode information for proteins.
IIRC RNA is made up mostly of the same nucleic acids as DNA. T (something something) is replaced by Uracil. The main difference is that DNA is double stranded whereas RNA is single stranded. Since mRNA uses three acids to represent one of the amino acids that make up the proteins it encodes, and there is a finite amount of amino acids, this means no new proteins are encoded if you add more "letters" to DNA/RNA.
Possibly the RNA could have some secondary function in the folding of the protein or as a complex inside it...