So would the seed keys or private keys for the segwit wallet created in Electrum work on other bitcoin apps?
seed phrase (mnemonic) no, because Electrum uses a different way of creating those words that no other wallet supports (one or two may let you import the same seed but it won't be their default settings).
private keys yes, because private keys use a universal format (WIF) that is recognizable by all wallets but you may need to take additional steps to let the wallet know what type of address you were using (the part before the colon)