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Transaction fee is quoted in natural numbers, e.g. 97 sats for a transaction. A fee-rate sat/vbyte is derivative and doesn't exist on the chain. There isn't any rounding problem.
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Just because something is derivative doesn't make it not not real.
At some point the price for 97vbytes and for 98vbytes would cost the same price. Alas, this isn't a "problem" per se but what would that look like tho.
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At some point (a pair of distinct fee rates) the price for N bytes and M bytes can cost the same price.
Example:
Tx_A is 1,000 bytes pays 1sat/byte
Tx_B is 500 bytes pays 2sat/byte
Both cost 1,000 sats
I suppose your example for 97/98 bytes would look similar.
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1 sat/vbyte is a clean and round number. What would less than 1 sat even mean? What's when you use an odd number of vbytes? Buy more unused vbytes to fill out a whole sat? or round the fees up/down? ceiling? Is there even pricing pressure here, do miners want to sell block space for less?