Your Dijkstra is implemented wrong:

 1 while(!pq.empty()){
 2     auto temp = pq.top();
 3     ll u = get<1>(temp);
 4     ll half = get<2>(temp);
 5     pq.pop();
 
 6     for(auto p: edge[u]){
 7        ll v = p.first;
 8        ll w = (half ? p.second / 2 : p.second);
 9        bool nex = half | check[v];
10        if(dis[type][v][nex] > dis[type][u][half] + w){
11            dis[type][v][nex] = dis[type][u][half] + w;
12            pq.emplace(-dis[type][v][nex], v, nex);
13         }
14     }
15 }

It's possible that for any given vertex $$$v$$$ and horse thing $$$half$$$, multiple triples $$$(dist, v, half)$$$ get pushed into the priority queue — the cheapest one and ones that the algorithm discovered before that. Each of these triples is eventually popped from the priority queue, and thus for each vertex, we look at its outgoing edges many times, not just once as Dijkstra is supposed to work.