I get out of the saddle a lot for multiple reasons. One is to give my knees and legs a break which seems to be the opposite advice from others. Oh well, works for me. My loaded riding is much more in the back. Heavy dense stuff goes in my medium handlebar bag but still no match. The first times I get up it feels different but I get used to it right away. On the flip side.. the first time I switch back to regular ride mode without bags and stand up I flop and wobble too. I compensate for something that isn't there now. Go figure. My bars are 440 24° flared so relatively wide but not MTB wide. For no particular reason but chance I haven't been on anything but an AL bike for many years to compare. My "touring" bike is not special purpose and it's my everything bike. An average gravel bike with a cheap relatively heavy frame with rear mounts but it works for what I do.

Staying on topic.. My difference in loaded and unloaded feeling seems to be me taking a little time to adapt and compensate, not the bike itself. I guess I've avoided noodlers or just adapt.