My gamertag has numbers next to it despite not being taken

Yes, the symbol would be the reason. That is also new to the update and is not something available through the old system.

https://support.xbox.com/my-account/manage-gamertag-and-profile/gamertag-updates-faq

Can I still get a new gamertag without a suffix?

Sure you can! There are still plenty of unique, 12-character-maximum gamertags that don’t require a suffix.

Note that only gamertags made with Latin-based alphabets (derivations of A, B, C, D, etc.) are eligible to be new gamertags with no suffix at this time.

As Smwutches said spaces and capitalization do not matter with gamer tags in the system.

The reason it would not have shown up for you is that when doing the search you have to type it in EXACTLY as the person typed it in when they set it up other wise it will show up that it is not taken.

How come when I search for that tag, no one shows up?

I wanted the name "Not A Snack" and I even searched beforehand if someone else already had that name. But I still ended up with numbers after my name despite only using letters. Could it have been the spaces in my gamertag that caused me to have
a suffix?

Nope it wouldve been because it was taken

When searching for a name you MUST have the exact context to find it

So it could be any million of combinations

Of spacing caps etc

It doesnt matter as the system sees it as the same

You really really didnt think a simple common namr like thst wouldnt have been taken already?

I have looked and did see another person named that.