Since you mention active shooter, you could consider a military individual first aid kit (IFAK) ripoff: https://combatmedical.com/product/march-ifak-resupply.
The above is high quality stuff, though a little spendy at $150 for just the supplies. For something cheaper yet still provides some trauma capability, Adventure Medical Kits offers the "Trauma Pak" which usually goes for about $25 depending on where you find it.
Obviously a little different from the more professional version up top, but on a budget some gauze and duct tape can indeed replace a wound wrap. You can also MacGyver a chest seal from the duct tape and plastic bag. I have a few of these packs that I keep in various places like camping gear, car, work desk, etc. Toss in a tourniquet and you can reliably keep someone from bleeding out from a limb, and provide at least some care for bleeding wounds elsewhere.
As a soldier who has friends at the base hospital, I keep the following in my backpacks and those small pockets at the bottom of my uniform pants:
With that bare minimum, I'm positive I can keep someone from bleeding out due to nearly any single limb injury and I can provide some help for a torso or head wound, though only some. But that's the goal, stop the bleeding and call 911.
In addition to my pockets, backpacks, and little trauma paks, I have a big aid bag that I keep in my car with just bleeding control stuff. Everyone says I'm crazy when they see how much stuff I have and ask something along the lines of "do you really need all this?". I then show them this video. Back then I only had a army combat lifesaver bag (enough for 2-3 really banged up people) and other random bits in the car. The second person to exit the crashed vehicle had a deep gash in her arm that started bleeding heavily; she also started going into shock. I used quikclot and an emergency bandage to get the bleeding under control, then laid her down in an emergency sleeping bag and propped up her legs to help with the shock until EMS arrived.
The only other time I've used my supplies is when an old lady had a nasty fall near my office. She had a pretty bad gash on her head which I was able to stop bleeding with a quikclot dressing and rolled gauze wrap. A friend then took her to the hospital.
It's never a bad thing to be prepared to help yourself or others. Just make sure you know how to effectively use the stuff you get. A Red Cross first aid or first responder course could be just as valuable as the supplies you purchase.
Edit for a bit more info. Don't get wrapped up in fancy gear (like iTClamps), odd ends (like eye shields), or especially anything beyond your capability to confidently use. In a big city, EMS is minutes away at all times. You should only need to worst-case prepare for something that can kill within that timeframe and that you have the capability to help with. The only gear you'd need as a first aider is bleeding control and maybe a CPR mask, because that's realistically all you're going to be able to use on a victim.
Your most important skill as a first aider is going to be calling for help and clearly communicating the situation and location. Again, this is your most important skill as a first aider: ensuring that professional help is on the way. Anything you can responsibly do beyond that is delicious icing on the cake.
I'm a backwoods hiker first and a prepper second, so my opinion of your list is coming from a different perspective (ie. living in the woods for a couple nights vs. long term sustainability). However my overnight hiking bag is my "bob" since they basically serve the same purpose.
I'll just port over your list since I can't listen to the video right now (forgot my headphones). I had to remove your vendor links as this sub doesn't allow link shorteners.
10: Wool Blanket by Ready First Aid -- $24.99
9: Slingshot by Marksman -- $18.73
8: Tarp by Stansport -- $19.99
7: Titanium Spork by Light My Fire -- $19.49
6: Pocket Stove by Esbit -- $17.05
5: Folding Saw by Mossy Oak -- $24.99
4: Stainless Steel Cook Set by Stanley -- $21.92
3: Ferro Rod by überleben -- $24.00
2: Water Filter by LifeStraw -- $24.50
1: Companion Knife by Mora -- $26.00
10: Wool gets wet, takes a lot of space and loses a lot of heat. Look into a bivvy sleeping bag instead ($8 on sale)
9: I've never seen the point of these, but to each their own. If it's for defense I'd suggest going with a pepper spray instead (easier to aim, longer sustained use, doesn't require reloading or ammunition). If it's for "hunting" then I'd just go with fishing line and a compact rod instead. Again, personal preference. You'd have to be a crack shot to ward off a bear or cougar with one of these.
8: $20 for a tarp is ridiculous. You can get an entire emergency tent for the same price. With no paracord in your kit your tarp isn't going to do shit.
7: $20 for a spork? Amazon has fire resistant BPA free plastic ones for $1.99.
6: These things SUCK! They never burn long enough, but you don't have any food in your kit regardless. Once you're out of fuel you're hooped, plus you don't have any firestarters in your kit (I see the ferro rod, but that'd take an intermediate material to transfer a flame. Good luck if it's raining).
5: Get a machete instead.
4: Paired with 6, you can get a lightweight combo like this which only needs a $4 butane / ethylene fuel canister to operate. It'll last way longer than the fuel pods that come with the pocket stove you've linked.
3: Get a USB arc lighter instead. $20 for a ferro rod is also ridiculous, you can usually get a pocket knife and rod for less.
2: Without a water bottle (metal, single walled) a lifestraw is beyond useless in a backwoods situation. A sawyer mini costs like $8 more (I know this doesn't work with your $25 budget, but I might just leave a filter off your list if that's the case, or link a quart bottle and some purification tablets).
1: Mora is a good brand, but I don't see much use for a 4" knife. If this is a budget built then get more millage out of your purchases by avoiding name brands and go for a $25 multitool with a small knife attachment like this peice of crap. Either that, or get a useful 6"+ blade which can actually be useful for defense.
I understand this isn't an exhaustive list of things to put in a bag, but IMO by going for a "budget" of $25 you've missed a lot of stuff. Most of the $25 things you've listed can have their tasks replicated by items which cost a fraction of what you've linked. Many items you've got just aren't necessary (I've probably done 300+ overnighters and I have NEVER said "darn, I really wish I had a (bushsaw, ferro rod, slingshot, 4" knife)"). So 4 of your 10 items aren't necessary. The other 6 aren't optimal. Maybe you'll change my mind when I can listen to your justifications for choosing these items over the alternatives. Look at lightsource(s), a solar charger and a crank radio, which do exist in the $25 range. Sorry for shitting on your list! IMO I'd try a "basic bug out bag for under $250" themed video over focusing on the individual cost of each item.