I don't quite have enough reputation to leave a comment but, @Joe batters are not obliged to get out of the way. As stated on UmpireBible Rule 6.03(a)(3), a batter is considered out if
He interferes with the catcher’s fielding or throwing by stepping out of the batter's box or making any other movement that hinders the catcher's play at home base.
As stated by UmpireBible (again) in a write up, there is somewhat of a gray area here in the rule book about batter interference. While the rules state the Catcher has the "right of way" and should have a clear path to make whatever play he feel necessary, you can't expect the batter inside of the batter's box to "just disappear" from the play either. Another quote from the UmpireBible
The emphasis is important because "any other movement" covers a lot of ground. A lot.
Point is, the batter is not required to get out of the way and from my interpretation, SHOULD NOT get out of way. From my own encounters (played baseball for 15 years) I personally never left the batter's box when I knew a throw down to third was happening while I was batting. In fact, most of the time I saw it happen, I believed the batter to inch forward towards the pitcher if anything to not get domed in the helmet by the catcher throwing down to third.(Somewhat disproving your theory that the batter's handedness influences the steal percentage of third.)
As far as the answer to your question(sorry for the small rule lecture), there are multiple factors influencing the steal rate for third base being a few percentage points higher.
While the throw down to third base is shorter for the catcher, catchers have less experience making the throw down to third base thus it is more uncomfortable for them.(Catcher SB Attempts Against) Pitchers have a harder time "holding" the runner on second base for similar reasons. Pitchers do not make throws to second base very often and do not practice holding runners on second base very often as opposed to throwing over to first base. (Pitcher Pickoff Attempts)
Catcher Pop Times
Runners are less expected to steal third base which might make it more of a surprise, in turn the runner throws the catcher off resulting in varying pop times (The time it takes for the catcher to catch a pitched ball and throw it down to the base, second or third) that are apparent in the Baseball Savant link in the previous paragraph(Catcher Pop Times). While all of this is true, the pop times are still significantly slower to second base as opposed to third base (about .5 second or 25% slower) so my previous statements don't fully explain the reasoning behind third base having a whole 3% higher success rate.
Taking a Lead
Runners are not able to take as big of a lead off of first base than they are second. While having a left handed pitcher on the mound presents the obvious challenge a baserunner on first is presented with, (the pitcher is looking right at them) taking a lead off of first base is harder because the first baseman is almost always "holding" the runner on by standing on first base itself. Whoever is tasked with holding the runner on second base, either the shortstop or second basemen, NEVER stands directly on the base and rarely comes over to "hold" the runner on the bag. In turn, the baserunner on second base is normally able to take a bigger lead (I struggled to find direct statistics on this).
There are a few other factors that might lead to this as well. Since third base is perceived as "harder to steal", only the fastest of runners are even attempting to steal third base. Thus they bring the average up and result in a higher percentage. Another factor is just the small sample size. While your statistic is shown over the course of 4 seasons (1998-2002), third base steal attempt data is only 10% that of second base steal attempt data. Lastly, somewhat building upon what I said earlier, pithers make more errors picking off to second base thus don't do as good of a job as they at first base. There have been 12 pick off errors this year(2022), and almost half of them (5 out of 12/ Pitcher Pickoff Errors) have been to second base even though pitchers pick off to second base significantly less.
Sadly I could not find exact data representing the information you are seeking. There are a lot of factors that are influencing the third base stolen base success percentage being a little higher than first base stolen base success percentage, but I do not believe the elevated success rate could be tied to the batter being a hinderance.