After cleaning our wooden cutting board, we using wipe it with mineral oil to help preserve it. Today, we accidentalky sprayed Weiman Stainless Steel Cleaner and Lolish on it instead of the mineral oil. The bottles looked similar. We quickly washed it with hot water; then after checking the inernet washed it with sea salt and also put baking soda on it to hopefully absorb any of it. We are still not sure if that's enough to prevent any potential poisoning with a next use. Can you please advise if it's okay to use again? Do you have any further recommendations?
I am surprised at your extreme reaction here. This is a simple cleaning product, so even if you have no further information, the default assumption is that it is not especially toxic. OK, some cleaners are corrosive, but this means you shouldn't be touching them in concentrated form, they do nothing in trace amounts. Also, there is no reason for the sea salt to somehow make it cleaner, or for the baking soda to absorb it, these washes would have been useless if it were highly toxic.
For the specific product you mention, it was very easy to find the safety data sheet. Its main ingredients are ... mineral oil, and related petroleum derived products. So, if taken by bulk, it is practically the same stuff you wanted to apply to your board in the first place. Of course, this is not the complete list of ingredients, and in theory, something dangerous could be present in small amounts - but this being a data sheet, it also gives straight information on toxicity. The worst thing in the symptoms is that it "may" cause nausea and vomiting if swallowed, but not to forcefully try to bring it back if accidentally swallowed - this is similar to what one would expect of mineral oil. And then there are the toxicity numbers: you need 2 g per kg, or 140 g for an average human, to cause acute toxicity symptoms. That is, if you drink less than a teacup of it, you are unlikely to even notice it.
Based on that, I would suggest that you just continue using your board as normal.