I'm reluctant to speak for Sparkfun. Even if I did have some insight, the situation can change rapidly.
But I can speak for PJRC. I can tell you we put a 1st moderately sized batch of Teensy 4.1 into production on June 23. Some were completed early and we started shipping backorders on June 30 and July 1-2. On July 6, we started showing it in stock on the PJRC website. The majority of that first batch shipped between July 6-16. As we shipped those, new orders came in from almost every distributor. We sent many to Sparkfun and a good number all the others. Today we're allocating the last part of that 1st batch (only a small number will remain here for orders) to Sparkfun and pin soldering. Whether the Teensy 4.1s we're shipping this week will be enough to clear all of Sparkfun's backlog (early next week), or if they get more orders before those arrive, I can not say. The best PJRC can do is manufacture, test, package and ship as fast as our process allows. That's what we're doing.
I can also tell you we put a 2nd large batch went into production on July 9. Normal production takes 3 weeks. So by the first & second week of August, we should have plenty to clear all of the non-pins backlog. I'm hopeful we may start to get some of that 2nd batch early, in which case we'll start shipping them on July 26. But when some are ready early, it's usually only a small part of the batch. Then the rest gets completed over the next 3-4 weeks, with approximately equal portions of the batch ready each week.
Soldering of the pins is starting this week. It's a very labor intensive process. Only so many can be soldered each week. We probably won't manage to clear all the soldered pins backlog until September.