RAW, there is no reason that it does not work
Tiamat is huge and would not be entirely within the 10 foot radius of the created door.
RAW generally considers that a creature is affected by effects that overlap it, even though it does not fully engulf the creature. For example. a fireball deals all the damage, even if it only hits the corner tile of a gargantuan creature.
On her Rise of Tiamat block of statistics, she has magic immunity limited to level 6 and lower spells. Since a holding bag is an unusual magic item, it would be logical to be immune to this effect as well.
The astral tear is not a spell, so spell immunity does not help.
She is a minor deity, so she gets a pass for things like this.
It is not protected by the rules, although it is a reasonable internal decision. I'm not sure I can enforce it myself. However…
Tiamat could probably escape quickly enough
Tiamat herself has no ability to move from one plane to another, but her raw power is still sufficient to make her a peak predator in the astral plane. Its extremely high intelligence score also allows it to move faster than most creatures that find it. It would probably not take him long to find a creature who knows the astral plane and the planar gates and gently persuade said creature to allow Tiamat to return from the astral plane. Given the potential utility of bonding with a god, I would not be surprised if such a creature is even looking for it!
This might well be a matter of days or even weeks, but if the group can not find a new pair of sacks at that time, they will face an angry dragon goddess once she's Will be back …