So you are saying that an umpire is *only allowed* to give warnings for the first disturbance?
Yes, that is correct.
If we start in HMO, it says:
12.1.4 The umpire must never award points for reasons that are not supported by the laws, perhaps
because he or she considers that one player “deserves” a point or that another should be
penalised for an unfair action. The umpire should always be able to justify any decision he
or she makes by reference to a law, and it is for this reason that he or she should study
carefully and understand all of the reasons for which a point may be scored.
If we go to the law 2.10, it says how you score a point:
2.10.1 Unless the rally is a let, a player shall score a point
2.10.1.1 if an opponent fails to make a correct service;
2.10.1.2 if an opponent fails to make a correct return;
...and then the few situations otherwise
-obstruction
-deliberate double hit
-strike with a side without ITTF-rubber
-moving the playing surface
-touches the net assembly
-free hand on playing surface
-out of sequense in doubles
-expedite
-para/wheelchair: no contact with the seat
-para/wheelchair: any hand on table before striking
-para/wheelchair: footrest or foot on floor during play
-para/wheelchari: chair or foot crossing the center line
2.9 Tells us the 8-12 reasons for a let. This includes disturbance that makes the opponent miss, if the conditions are disturbed in a way that it could affect the outcome of the rally, and to warn or penalise a player or adviser.
Well, then how can you penalise a player or adviser? Then we are in 3, the regulations for international competitions. We are in 3.5.2, where we find the yellow cards, yellow/red, penalty point system and calling the referee to stop the match. For context - shouting is normally considered less serious (=PPS), but of course there could be situations where it is considered serious (call the referee - red card - stop the match):
3.5.2.2 If at any time a player, a coach or another adviser commits a serious offence
the umpire shall suspend play and report immediately to the referee; for less
serious offences the umpire may, on the first occasion, hold up a yellow card
and warn the offender that any further offence is liable to incur penalties.
3.5.2.3 Except as provided in 3.5.2.2 and 3.5.2.5, if a player who has been warned
commits a second offence in the same individual match or team match, the
umpire shall award 1 point to the offender's opponent and for a further
offence he or she shall award 2 points, each time holding up a yellow and a
red card together.
3.5.2.4 If a player against whom 3 penalty points have been awarded in the same
individual match or team match continues to misbehave, the umpire shall
suspend play and report immediately to the referee.
So, yes, the normal in this situation will be: Let, yellow card, replay the point.
As for "you almost never replay the point", this is correct outside of the 8-12 reasons for let in 2.9. Typical if there is an edge/side, hit/miss, obstruction/not obstruction, there is only point to A or point to B as the options. But this is totally different from e.g. let for disturbance + let for warning a player.
I hope this helps.
Kind regards
