It might be worth adding that Network Rail operates on 5-year plans and budgets agreed with ORR (Office of Rail and Road) which is the industry Regulator.
Their funding and priorities are essentially set by government via DfT and ORR, and they are government-owned.
NR collects a major part of its revenue (access charges) from the Train Operating Companies, of which GTR is one.
GTR, like most train operators, was a DfT franchise operation until revenues were hit by Covid, and is now on a short-term service contract with DfT pending the creation of Great British Railways (GBR) later this year.
GTR is a private company, owned by the UK's Go Ahead group and France/Canada's Keolis.
They pay NR to operate the infrastructure on its service network, and they work very closely with NR.