Here's a visual of the gap

Why do you feel a need to fill it? Won't the backsplash cover it?

1/2 in deep and tall hole not too deep? Backsplash would have nothing to fall on.

Caulk wouldn't work in any event, but yeah, I'd just fill it with thinset.

Why wasn’t the bar substrate prepared to actually be flat and level fir the counter to sit on properly? That is your issue. I do hope that it is properly supported with steel, or you will be removing that to correct that too. What IS it even contacting if it isnt sitting on the pony wall properly?

If that's drywall, I'd use a setting type of joint compound to prefill.

https://www.homedepot.com/p/USG-Sheetrock-Brand-18-lb-Easy-Sand-20-Lightweight-Setting-Type-Joint-Compound-384214/100321609

I really don't think you need to worry about the gap. Tile will cover it up.

But, since it is bothering you, you could use some foam caulk backer rod.

Or low expansion polyurethane insulating foam--mask carefully all of the surfaces where you don't want the insulating foam & WEAR GLOVES!

Or add another layer of 1/4" drywall

Or a layer of 1/4" tile backer board

Or remove whatever is back there and install a piece of 1/2" tile backer board.

@User Very astute observation. Sadly one of the interesting things about living in a 50-year-old condo is that nothing is level with each other or within itself. Such is the case with my breakfast bar after the tiled bartop was demo'ed. The wooden top horizontal beam of the pony wall sits about 1.5 inches lower from the other side, with one end rising above the drywall it's sandwiched between, and the other end sitting below. It's a very dense wood (oak?) and even masonry drill bits got worn out quickly. And there are a bunch of large-headed nails over the top of it. So the decision was made by the countertop installers to shim everything. I did not like the L brackets they offered, so did my own stealth brackets - creating a deeper channel on the higher end of the pony wall and gradually shallower channels to no channels on the low end and added some wood shims as that end of the wood beam was sitting below the drywalls. It was a lot of work for first-time DIYer but I managed to have all 7 stealth brackets sit level with each other on this wonky wall (I know it's overkill, but I'd rather have that than worry about a falling or cracked quartz countertop later). I used 3 inch long screws - 28 screws total. I also made the end of the brackets slightly higher compared with the screwed end, as recommended by various pros I read about on the internet. So, I really hope that countertop is not going anywhere. I thought the installer would level with a ton of wood shims, but turned out he shimmed only with caulk! He used at least a whole bottle of DAP Alex Plus Fast Dry 20min Latex + Silicone caulk while he was here. That was how he shimmed my kitchen cabinets as well. Anyway, so what's UNDER the breakfast bar right now is a mix of stealth brackets, pony wall wood support beam, a ton of caulk, and dry wall. On the kitchen side, that gap I am referencing is the other dry wall that sandwiches the wood beam.

@ci_lantro @bmorepanic @PPF. Okay, so it looks like I have a ton of choices here. What's the best all-around choice considering that I live in a condo with minimal storage space so would prefer to avoid large bags of joint compound if I can. I have other areas to patch up, such as an old unused landline phone box to fill, and walls behind former laminate backsplashes I need to smooth over before tiling, etc... What is something I can use for all of those applications without too many extra leftovers?

Would this work? Amazon.com: 3M High Strength Large Hole Repair, 32 oz., Fiber Reinforced Spackling Compound : Everything Else

Or this? Amazon.com: 3M High Strength Small Hole Repair, Primer Enhanced Spackling Compound, 32 oz. : Everything Else

Or just buy a smaller bag of joint compound? Westpac Materials 4.5 lb. Fast Set 20 Lite Setting-Type Compound-55330H - The Home Depot

Haven't used the 3M product.

The setting type drywall compound will do the job.

If you are a novice, I suggest using the 45 minute setting compound. Be aware that you will probably mix up more than you need or it will start to set before you get the job done and you'll have to toss the mixed compound. Once it starts to set, it is unusable. So I would suggest buying a larger container than that 4.5# one. It is cheap so you won't feel like you have to save the leftovers.

@ci_lantro I ended up using U S GYPSUM All Purpose Joint Compound from Lowe's due to the rave reviews regarding ease of use. Covered up enough of the gap. Now the hard part will be the nearly endless possibilities for backsplashes!

I understand. But it makes me feel better, and in any case I needed to fix other parts of my dry wall. So no material wasted as I have a whole bucket to use up anyway.

Soulflowerpetals, here is a link explaining the differences between the various drywall compounds, starting with the difference between 'hot mud' and premixed. For future projects...

https://drywall101.com/articles/types_of_mud.php

ci_lantro, thank you so much! Very helpful info. I'm saving it in my ideabooks for future reference. 😊