My PhD supervisor is against external collaboration. What should I do?
Since you wrote that you are funded by a project, I'd like to mention one possibility, without knowing whether that's really the reason or not.
Project funding, especially for more applied funding schemes (e.g., EU Horizon 2020), typically come with obligations, such as reporting, or having to work on certain problems that were promised to be worked on in the funding proposal. This is possibly a reason for why you are working on a topic that neither your advisor nor other group members can help you with: because it has been promised in the proposal for some reason.
Now as you mention your best bet to get support is by collaborating with externals. Scientifically fruitful collaboration is often quite dynamic: the actual research question addressed may change a bit during the collaboration, and in particular it may move away from what was promised in the proposal. From a scientific point of view, this is how great ideas are developed, but you end up getting results that your advisor (grant holder) does not know how to sell as fulfilling the obligation that comes with the project funding. Also, you may end up getting results that your advisor may be unable to use as a proof of competency for future funding proposals, which is important to maintain the flow of funding.
Both of these would be problematic for your advisor, which is why he/she may be unwilling to give up control over what you are doing by letting you collaborate with someone not under his/her control. Also, once a collaboration has been started, if would be problematic for your advisor to ask you to end the collaboration if he/she later gets the impression that the focus of the collaboration is not what he/she needs or wants - at that point your potential collaboration partner already invested time, which has to be respected.