Travel kit

Oh man, this is my specialty. One of my favorite types of vacations is just holing up in a gorgeous, remote cabin for a week and taking all my fancy food plans with me that I normally don't have time to execute in my day to day life. And like you've experienced, it's difficult to predict what an Airbnb will provide. Even if you ask the host, sometimes the items won't be up to my standards (often understandably, as I'm a bit picky in the kitchen.)

Your list is great, and probably good enough for most purposes. I would add:

• A safe container for the knife. We use a random box that a small electronic came in, with a hole cut out for the handle of the knife. In the past I've wrapped knives in an old towel with some duct tape to secure it.
• If I'm not packing light, I bring a cast iron pan since they're so versatile.
• Sometimes I'll bring a large stainless steel pot, since it's simple and I can both saute and make soup or chili in it. It's large, but you can put smaller items inside it to save space.
• The smallest grade of cheese grater, obviously for cheese, but mostly because it works for zesting citrus in a pinch.
• I like to make Chinese food, so I bring tiny jars of dark soy sauce, sesame oil, and chili crisp. (Try to think of things that might be staples for you, but aren't staples that an Airbnb would provide, particularly for different cuisines.)
• Deli containers for storing leftovers. They're cheap, light, and stack/store compactly. (I usually don't throw them away, but it's no sweat if you feel like dumping these in the trash if you're in a rush leaving an Airbnb. They're just takeout containers.)
• Since I can't plan for every spice, I usually like to bring taco seasoning, chili seasoning, and a versatile spice mix like Old Bay.
• Hand blenders are fairly small and very versatile. I find that most Airbnbs do not have blenders.
• Plastic nesting mixing bowls, bonus points if they're the type that come with matching lids to store leftovers.
• One decent silicone spatula.
• Chip clips and/or rubber bands to close opened packages.

Also, I've been eyeing this kitchen multi-tool for a while. It may be more necessary for campsite cooking rather than Airbnb cooking, but it covers your cheese grater, citrus zester, bottle opener, can opener, wine opener, garlic crusher, peeler, and a few different small knives, all very compactly. So it's more designed for this purpose than a normal multi-tool, although those are convenient as well. (It also has utensils, but obviously those are provided in Airbnbs.) It's a bit pricey, but if it's sturdy it seems worth it. I can't report on the quality since I haven't purchased one yet.

As a random tip, I'd recommend getting a "travel kitchen" plastic tub, so you don't have to collect these items each time you have a trip. And whenever one of your kitchen items wears out a bit, throw it in the travel tub if it's still usable. Some things aren't nice enough for me to want to use every day, or I've replaced them with higher quality items, but they're good enough for a weekend at an Airbnb. Helps cut down on cost and waste.