How many addresses are there now with segwit? Could you help me understand if with segwit activated do we have more available private keys and addresses in the Bitcoin universe?

With Legacy [1...], Compatible [3...] and Bech32 [bc1...] addresses do we have 3x more possibilities ?

Thank you.
There are 2160 P2PKH addresses.
There are 2160 P2SH addresses
There are 2160 P2WPKH addresses.
There are 2256 P2WSH addresses.
There are 16 defined but unused witness versions which can be encoded by BIP173 (Bech32) addresses, each with data length 2 to 40 bytes. That's 16*256/255*(25640 - 256) =~ 2324.006.


That's 2144363455669619533814323684450670475181580230986810095535626033037852598144837730344835022389248 in total.

The number of private keys has not changed; that's still slightly less than 2256, namely 115792089237316195423570985008687907852837564279074904382605163141518161494336. Only the number of ways to use them increased.