I am going to provide a rough estimate of this effect.
This study shows that Covid-19 deaths are roughly 50% higher per-capita in the most Republican-leaning counties versus the most Democratic-leaning counties.
I am going to use this to compute a rough estimate of the impact on elections. For every 5 voters that die, assume 3 are Republicans and 2 are Democrats. (That is a 50% higher per-capita rate).
I this provides some easy math. For every 5 covid-19 deaths, the Democrats gain 1 vote. So, you take the number of deaths and divide by 5 to determine the relative gain in votes.
North Carolina, my state and a swing state, has had about 20,000 covid-19 deaths. So the gain in voters is about 4,000.
That is a very slim margin, that would only affect state-wide elections that where well within the recount margin. Looking at the 2020 elections, the only race that close (that I know of) was the North Carolina Supreme Court Chief Justice race that was decided by about 400 votes.
Scaling this down to a congressional district, the gain would be around 300 votes. It would only make a difference in a very close race. In 2020, New York 22nd was decided for the Republican by 109 votes and Iowa 2nd was decided for the Republican by 6 votes. But 2 close elections in one election year is historically high. The average is closer to 0.25 per election year. That’s a 1 in 4 chance it will happen in 2022.
Of course the estimate is very rough and there are many potential biases. The actual gain is probably much less than 1 in 5 deaths because that assumes every death was a likely voter.
Edit: Another bias is that I used all deaths. The rates were similar before the vaccine, all the divergence was after the vaccination rates diverged. If I adjust for that then the divisor becomes 4 rather than 5. The simple math implies a gain of 5000 votes in North Carolina.