Definitely hold on to it. Carriers that are rapidly adopting 5G are having all sorts of growing pains. Congestion, interference causing a reduction in range, 5G not moving between towers. Goto settings, general, about and tap on carrier version a few times as sometimes that will for an update if its available. Also turn off 5G just to test out connection stability.
Cellular connections aren't like FM radio. Your iPhones reception to a cell tower is determined by data the cell tower is sending it. Your iPhone will initially connect and sends its reception strength and quality (noise level), the cell tower sends back adjustments for the for an optimal connection.
Too much power reduces the quality because the connection gets too noisy from interference plus it kills the battery. However cell carrier want to use the least possible because its frees up room for more connection on their network hence the ever degrading standby signal reception.
Matter of fact anymore as you near a cell towers boundary even without a another tower to hop to the connected tower will let the connection drop instead of increasing power to prevent interference outside of their boundary. So if you noticed small gaps between towers occasionally, now you know why.
The iPhone 13 Mini has 4x4 MIMO so 4 antenna for LTE and 5G and like the iPhones before it the RF has been reduced to get to Apples standard 1.2 and 1 Specific Absorption Rate.
www.apple.com
So even a "not as good" design like a shell that isn't as RF transparent makes little difference, its output power is just reduced slightly less to account for it. Things do happen though, maybe your holding it wrong? 😅