The bearing retainer on yours looks nice and flush, or at least near to flush as mine does.
I loosened my retainer up a little and then put the buttons back on and was able to nearly recreate the sound you are getting. This is why I thought maybe your bearing retainer was not screwed the whole way down. However, again your retainer ring looks pretty flush.
As far as wobble goes, yours looks just about the same as mine does. I would say the wobble is no big deal but it could be part of the issue.
Perhaps you're buttons were manufactured a little out of spec.. It wouldn't take much for the button to rub against something if that was the case..
You would probably be able to see evidence of this on the inside/back surface of the buttons. You would see scratch marks in a circular pattern relative to whatever the button is rubbing against.
I suppose it's either that or maybe a bad bearing.. If it's a bad bearing your kind of screwed because this spinner uses a non-standard bearing. It would probably be very hard to find and replace. If you got this thing through Amazon though, you could just return it for a replacement.
On the other hand, if it doesn't bother you that much and it isn't slowing the spin down negligibly, then keep it and maybe consider trying another new one that doesn't cost too much.
If you like the size and shape of this spinner, then you might like something of a similar size and shape, but in a heavier material. Titanium is a very light metal, as is aluminum. For something inexpensive on the heavier side, you should maybe look for something in brass or stainless steel.
Here are a few I found that are inexpensive and well-made and, most importantly, have a bearing retention ring with a slot!! 🙄
Also, all of these spinners all use a very standard and common r188 style bearing which are easy to find and replace.
First, here is a picture of them laid out beside the one you have, for size reference:
https://i.imgur.com/9MF52wi.jpg
Here's a brass one on Amazon:
https://www.amazon.com/dp/B06XXXNVNL/ref=cm_sw_r_cp_apa_i_vdYzDb9X57Y2M
Here's a few I have from our friend Josh. He's clearing out old stock and having a sale:
https://spinetic-spinners.com/product/2r-designs-circulator-spinner/
https://spinetic-spinners.com/product/2r-designs-trinster-spinner/#reviews_summary
https://spinetic-spinners.com/product/cigreen-mini-medic-spinner/
https://spinetic-spinners.com/product/axiom-spinners-tetra-spinner/
https://spinetic-spinners.com/product/kepler-very-dapper-spinner/
https://spinetic-spinners.com/product/tobeco-technology-mini-oculus-spinner/
https://spinetic-spinners.com/product/dual-dragon-aero-spinner/