Proof of Stake (PoS) offers several advantages over Proof of Work (PoW), especially when it comes to scalability. PoW requires miners to solve complex mathematical problems, which is computationally intensive and limits the number of transactions a network can process per second.
Sorry, this is incorrect (and I could bet I have read a very similar phrase on another website).
The mining process (calculating a hash based on block data) occurs entirely on the devices of the miner. It does not use Internet bandwidth which is the limiting factor for transaction throughput. The "network" has no incidence in mining, as it's not an interactive process where several miners need to coordinate or so.
While the miner also validates transactions (like all full nodes do) and this of course is a process which takes more resources if the throughput is higher, stakers in a Proof-of-stake environment must do the same thing, so this is also not something limiting the throughput in PoW.
The only factor where PoS achieves better results is latency, as I described above. This is however the result of a tradeoff: the validator "in charge" of the block is known beforehand, selected by a process influenced by randomness (e.g. the Follow the Satoshi algorithm). This however also means that PoS depends on the validators always knowing who is a validator, i.e. of the "permissioned" character of the network. In PoW instead nobody needs permission to mine - you simply find a hash or not, and if your hash meets the rules then you can just have started to mine without anybody having "invited" you.