In past US Presidential Elections, by how much have state recounts differed from their original counts? (in terms of absolute number of votes, but most importantly, in terms of percent of overall votes for that state)
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TL;DR
in the past 20 years, there were 3 US Presidential Elections with significant recounts in at least one state (2020, 2016, 2000), and
in all those cases, the net change on results at state level was smaller than a one twenty-fifth of one percent (the largest net vote change was approx. 2000 votes in Georgia in 2020)
2020
Georgia: On November 11, the Secretary of State of Georgia announced there would be a full recount by hand, and on completion, the Georgia margin of approx. 14,000 votes was reduced to approx 12,000 votes. The ~2000 vote increase to Trump's tally was approximately 0.04% of the state's (4,937,998) votes (or one twenty-fifth of one percent).
2016
In the 2016 US Presidential Election, there were 5 filings for recounts
Of the 5 filings for recount in 2016 (Wisconsin, Pennsylvania, Michigan, Nevada, and Florida) 2 were allowed to be recounted (Wisconsin and Nevada)
Wisconsin: Clinton gained 713 votes, and Trump gained 844 votes, resulting in a net gain to Trump of 131 votes (a net change of 0.0042% of the total vote)
Nevada (partial recount): Only De La Fuente was recounted (93,840 ballots in total), and after the recount Clinton lost 9 votes and Trump lost 6 votes, meaning the net change was that Trump gained 3 votes (a net change of 0.0032% of the total vote)
2012
No references to any state recounts for the 2012 US Presidential Election on its Wikipedia page
2008
No references to any state recounts for the 2008 US Presidential Election on its Wikipedia page
2004
There were recounts of 11 of New Hampshire's (~300+) voting wards.
In the eleven wards recounted, only very minor discrepancies were found
Note: wikipedia mentions other recounts in 2004 (involving districts in Washington and North Carolina), but I don't think any of those eventuated
2000
In the 2000 US Presidential Election, Florida was recounted. Bush had a 1,784 vote lead on election-night, and a 900 vote lead the day after election. Due to the closeness, a statewide machine recount was mandated, and it completed 3 days after the election reducing Bush's lead to 327 votes
After it become clear Florida would decide the election, a manual recount was requested in four counties
Bush won Florida .. by a margin of only 537 votes out of almost six million cast
Based on the above numbers, Bush's pre-recount lead was 900, and his lead after recount was 537, so the net change was around 363 (approximately 0.006% of the total vote for Florida)