Remove the Decimate modifier, it looks like it messes up your topology and therefore the interaction between the armature and the mesh. More generally, the rest of your topology is a bit too dense and not verty good, you should retopologize, then give a Subdivision Surface in order to smooth the whole shape.
Maybe you should work with less bones and segment them. But if you want to keep your current armature, you first need to create additional edge loops at the base of the tentacles, otherwise you won't be able to bend the mesh:
Once done, if you don't want to reparent the whole mesh, select all the tentacle bones in Edit or Pose mode, switch to Object mode, shift select the mesh, switch to Weight Paint mode, then in the header menu > Weights > Assign Automatic from Bones, this operation will recalculate the weight for the selected bones only (there may be a way to select several bones once in Weight Paint mode but I don't know the shortcut):
Edit: From your second file, first you need to disable the Deform option of the controller bones, otherwise they will act on the mesh:
To segment the bones, go into the Bone panel and increase the Segments value (like 3). You can select all your bones, type the value, and AltEnter so that it applies to all the selected bones:
Now you can recalculate the weights again. You may need to give some small corrections in Weight Paint mode. Then it works:
Also for tentacles, the Spline IK constraint is interesting, see my explanations here.