Bike seems less stable when using handlebar bag On a recent 3 week trip I used a handlebar bag (together with two back bags) to carry the stuff I needed.
In the handlebar bag I carried a reflex camera, my phone, a power bank and some candy.

While my bike normally feels really stable, the first few days with the handlebar bag were a nightmare: the handlebar constantly felt really wobbly, to the point I had to check it was not loose. Then I got used to the feeling, but still could not completely trust the bike.

Can the handlebar bag cause such behaviour, and how can I mitigate it?

Edit: I had a picture of the handlebar bag to give an idea of the dimension. About the mounting, the bag itself is firmly held on the handlebar, and also the content did not have much clearance to move inside, maybe less than a centimeter. The reflex bag basically left only the space for the smartphone.
Yes, the bag can cause the instability. The physics is quite simple.

Ordinarily, a bike is self-stabilizing. If you turn the handlebars to the left, you steer to the left and the bike leans to the left. However, the turning gives a centrifugal force to the right, which causes the bike to want to lean to the right which, in turn, straightens it out.

With a bag on the handlebars, things change. With the bike perfectly upright, the weight of the bag acts completely downwards and does nothing to turn the handlebars. However, as the bike leans to the left, the bag can lower itself by turning the handlebars further to the left.  If the bag is heavy enough, this effect will overcome the self-righting stability of the bike and now you have a system that responds to a slight turn to the left by trying to turn more sharply (positive feedback) rather than the usual situation of responding to a slight turn to the left by trying to go straight again (negative feedback). This is the instability that you felt while riding.