Looking for advice from veteran DMs

Welcome.

Let us see how I would handle it.

Let's first note - these are guidelines, not rules. For example: in my universe of D&D, Detect Magic is NOT a ritual spell - this saves all players from having to hear that one player spam "I Detect Magic," every time I speak, and Eldrich Invocation doesn't exist. Guideline changes like this ARE sincerely appreciated by ALL players at the table and makes the adventure much more challenging.

Thaumaturgy and Prestidigitation is just noise, light, sound, something annoying, odd, else fun to contend with for any NPC - just cause a character raises his voice or alters appearance of their eyes, for example, any NPC higher than level 3 are unlikely going to be phased by it, and not all NPC's are going to even care. For example: Bob, the innkeeper in a large city, might already be used to these tricks by customers coming and going - he is a veteran of this ploy, while Bob in the back woods of a small town, might declare witchcraft and alarm the towns folks of the evil that is inhabiting their tiny community - ringing the town's bell, rallying the townsfolks, "Kill the witches!"

Intimidation, Deception, and Persuasion skills are good when needed to scare, de-escalate, seek favorable conditions, to steal, etc. but you can have it NOT work. You are the Dungeon Master. Sometimes conditions aren't favorable (environmental conditions to accessibility). It's just that simple. Not every instance these skills will work: try to intimidate a guard at the gate or a bouncer at the local watering hole - they're used to people trying to brute their way, and a farrier, blacksmith or bartender - depends - though he or she already has had their share of sh###y customers, from bad attitudes to threats because customer isn't happy with something (billing, quality of work, quality of service, quality of product, etc.), so they too are NOT so easily pushed over by these intimidations, deceptions, persuasions ;)

Note, if you have bad players, consider going to meetup.com - create a group ($35 a month) - or join a group (free). My group is 24 players - I banned 3 of them for being annoying, while the group down the street from me has 3,000+ players (I prefer quality over quantity, and why I left that group with 3,000 players....story for another time). But at least you can pick and choose players you want who will appreciate your time and energy to tell them a story, else at least run them through encounters. Some players are socially inept, else just not a good fit for your style of gaming (worse, a player who just likes to cause trouble for you and other players).

 PS yes, get that book - its an easy, yet fascinating read, trust.