Split the Party as a teaching tool
There is a lot riding here on how the less-experienced players perceive their treatment by the more experienced players. Do your newbies feel like the veterans are patient teachers who want to encourage them into your social circle? Or is their experience that the others are domineering jerks who order them around because they 'know better'? That is the major dynamic that will decide whether your experiment is successful or not - but it is the part that is least under your control and not the point of your question. (also; we have questions about that if it is a concern of yours)
You have specifically asked about how to structure the plot so that you can run sessions that can act as new-skills tutorials for the new players but which don't bore the more experienced ones. That part is under your control, and it is my recommendation that you split the party for some of these sessions.
When thinking about the skills you want your new players to learn, structure your challenge to occur in four stages:
(1) a group challenge in which all of them participate (and ideally the experienced players are guiding the new players)
(2) a hard sub-group challenge for the experienced players (which the new players can observe)
(3) a soft sub-group challenge for the new players (which the experienced players can critique)
(4) recombine the groups for a final challenge in which the new players synthesize and apply their knowledge
You can run each of these in the order listed (but don't have to). You can have any combination of (1), (2), and (4) or leave one or two of them out, but you will always have (3).
Examples
trap-filled areas where perception is key
The party needs to recover the MacGuffin from within a trap-filled complex; but a rival group has arrived first. They enter the complex together, and together negotiate the dangerous entry chamber (1), or (if you are skipping (1)), in the entry chamber they find evidence of the rival group having passed - including evidence of the deadly nature of the traps. However, beyond the entry area there are multiple branching pathways - if they stay together, they will never reach the MacGuffin before the rival party, and they don't know which way they went. Because of the time element, they have to split up to make sure they arrive first. Flip scenes back and forth between the two groups, and make sure the inexperienced players are watching the experienced players model the skills you want them to try. After the experienced group has negotiated a series of hazards (2), it is time for the inexperienced group to try a few on their own (3). Eventually the experienced group reaches the MacGuffin, but they are soon set upon by the rivals, and have to hold them off for a number of rounds, fighting a delaying action, until the inexperienced group arrives and they finish the fight together. The two groups have both met challengers commensurate with their abilities, and hopefully the new players have seen skills modeled and then had the chance to practice them themselves.
powerful minibosses where teamwork/support spells are key
The party is traveling together from A to B and they are set upon by foes. There is a big group battle (1). If the party is escorting a MacGuffin (personage or object) it might get taken when the foes withdraw and the party has to follow up to recover it. Or they are simply out for revenge on the group that unjustly attacked them.
They follow the retreating group back to their lair / stronghold. But there's a problem; the foe has sensibly put multiple guards on watch with overlapping sight lines, so if the party together assaults a guard, the other(s) will see, retreat, and inform the lair. The party will have to split, approach the guards stealthily, and attack in a coordinated way to eliminate all the guards at once so that a warning cannot be raised. The guards will need to be taken out quickly by combining PC abilities, not by wearing them down through uncoordinated attacks.
You might do (2) and (3) in order, with the new players watching the experienced ones and learning from their tactics, but the experienced players facing harder or more numerous guards. Or you might do (3) first, with the newer players attacking the guards that are farther from the lair and then have the experienced players attack the guards closer to the lair (2). The second way, if the newer players partially fail, and someone 'gets away', it adds more foes to those the experienced players have to deal with in (2), increasing the challenge to their ability level.
After all the guards are eliminated, the party reunites to enter the lair and face the boss and their remaining guards (4).
Strategically splitting the party for specific challenges can thus be a way to provide difficulty levels appropriate to player experience and have experienced players model skills you want new players to learn. If you want, you can incentivize the new players paying attention even when it is not their turn by rewarding insightful observations or questions with experience points or Inspiration points.
Somewhat related and perhaps worth reading if you try this approach: Tasks for a split party
I haven't used such a technique myself as a DM, but it was used after a fashion in a group where I was a player. We were running 5e but the DM wanted a 'first edition nostalgia' feel for the game, and so was playing with 'training times'. All our characters had come together to a 'training school' when it was time to level, and we faced various skills challenges that were designed to help us (as players) learn our new class abilities. Sometimes our foes were inanimate (traps and such), sometimes they were rival parties, and sometimes they were each other. After each 'training session', the NPC trainers provided debriefs where they critiqued our characters' performance (and the DM offered metacommentary on our performance as players). While not occurring in the explicit stages I have suggested, it worked well as a model of designing challenges with specific teaching objectives for new character abilities and setting a narrative in which performance could be discussed and evaluated.