Is there a way to get on-chain through an Oracle the price of stkAAVE?

Well aaveOracle returns price of assets that are listed in aave protocol markets. Now, as per aave protocol price of stkAave is same as Aave token because in the staking module you can go stkAave to Aave and vice-versa 1:1

There can be price difference for Aave and stkAave tokens on secondary markets (for eg. uniswap liquidity pool, if there is one) and you can get that price from the respective secondary market oracles