A sloppy fit is a sloppy connection!!!
I'm aware of Battery Post Shims, but for now I'm using duct tape to hold it down because it's convenient for disconnecting/reconnecting.
No, no, no! You can't expect that to work! If you don't have a good physical connection, you can't have a good electrical connection. That Is Not Going To Work. Ever.
I'm sorry it works "sometimes" because it's misled you into thinking this even has a chance of being a good idea.
This is a reality-check to Stop Doing That.
In fact, you are arcing the heck out of the terminals on your nearly-new $150+ battery. Depending on the oil and grease level under the hood, you are also inviting an engine fire. Never do anything like this again.
Battery terminals are different sizes. On purpose.
The positive post is somewhat larger than the negative post. This is deliberate, so that when you try to install a battery backwards, the negative post won't fit and the positive will be exactly this sloppy. Since this wasn't a problem til now, perhaps this battery was mis-manufactured.
Note also that SAE batteries (designed to American market standards) have slightly larger terminals than JIS batteries. But you would then be having fitment problems on both sides, I would think.
Alternately, someone may have replaced the negative battery cable or clamp, and used the wrong one - either a cheap/junk/mail-order "universal" one, or one sized for the positive terminal. (e.g. because the auto parts store was out of stock of the negative in the needed length). If your negative terminal is red, that is surely the case. The prior battery probably had shims and you didn't notice when you removed it.
Any ideas what is going on here? Is simply tightening the connection the solution to my problem or is something else going on?
No, it's the garbage connection. Fix it directly.
Now, since you disconnect your battery every time you don't use the car (gee, wonder why the terminal got worn out), you should probably consider a battery disconnect switch instead. The cheaper of those simply clamp on the battery terminal and then have a post to attach the battery cable to.
Disconnecting the battery every week isn't helping
You are likely causing wear to the battery clamp and terminal by doing so. It may not be a coincidence that the one you regularly remove is also the one that is failing.
I disconnect the negative wire from the post after each use because the car sits 3-7 days between uses.
That ought to be unnecessary. If you are doing that because of something you heard, stop doing that, the person who told you that is dumb and owes you a battery cable.
If you are doing that because of direct experience of the battery being drained by parasitic loads on the car, that should not be happening. Troubleshoot that. Put an ammeter in series with the battery, with all things off. See what the parasitic current is (a few milliamps is no big deal; that's just clock and PCM keep-alive) and disconnect stuff until it goes away.
Start with anything plug-in, like GPS, USB chargers in a cigarette lighter (12V) port, dashcam, anything plugged into the OBD port. It may well be something stupid like your USB charger. If the car was ever bought used with financing, it might have a tracker which may be no longer relevant.
Anything that is on an "always-hot" circuit can always be moved to a different circuit that is "hot in run and accessory". On the newest cars, the 12V sockets have been moved to that, precisely because of USB chargers, navigators and dash cams draining batteries.
After that, start pulling fuses on things, starting with anything aftermarket like a subwoofer system.
Find it, kill it, stop pulling your battery cable.