My reading of the article is that it is Tawiwan who doesn't want Starlink instead of being denied by Elon Musk.
SpaceX dominates the satellite internet industry, and Mr. Musk has long done business in China through his electric car company, Tesla, which has a big manufacturing operation in Shanghai. Officials in Taiwan decided it would be best to build a satellite network they could control.
Besides, starlink isn't the solution for this scenario anyway. Any LEO communication network need numorous ground stations to connect to internet because their low orbit. One can bypass ground stations by intra satellite relys, but that will eat up the bandwith of the satellites which is share with a large neighbouring regions. This will chock the network to the point of close to a network shutdown which is not acceptable by neighbouring countries. Starlink works well in Ukraine because the sat overhead can reach the ground stations in Ukraine's western neighbours, but Taiwan's SE Asian neighbours are highly doubtful to jump in to the aid in time of crisis.
Taiwan building its alternative is just a joke, it can not afford the cost, nor does it have the competence. Their only chance is relying on US sat on higher orbit (GEO).