I am a highly skilled worker in the oil & gas industry. I fear I may be laid off soon because gestures at everything. I have already begun rapidly applying to a lot of jobs. Unemployment in my state, PA, will be enough to cover my mortgage, but not much above that. I do have a hefty emergency fund and a lot of money in the stock market, so I am in no serious danger. However, I would prefer not to utilize the emergency fund or pull anything out of the market if I can, so I am curious what I can do to supplement my monthly income?
You can certainly work food/package delivery or similar while still hunting a proper job to keep money flowing in. You could take on extra work now to supplement income if you were so motivated. If you do become unemployed there's often some disincentive to work part-time, so you'll need to weigh the cost/benefit of a part-time temporary job.
It's hard to know how long finding a new job might take, so I'd focus on the things you have greater control over now. Primarily this means cutting expenses. Perhaps you can refinance your mortgage, cut entertainment spending, etc.
You could go further and rent out a room in your house to help reduce living expenses or downsize. People have all sorts of creative solutions to low income, it's just a matter of how far you're willing to go to protect your savings.
You mentioned you are "highly skilled". Do you think your employer agrees, and if so, do you feel they would be reluctant to let you go, except that maybe they cannot currently afford to keep you? If you can answer yes to both of those questions, then you may benefit from discussing this with your employer.
Sadly, employers who let employees go solely because they can't afford to keep them, really ought to have a conversation with the employees first, but unfortunately not all do. You could consider initiating it yourself, perhaps with an offer of hours and pay reduction to help the company save costs. Even if you offer 90% and 1 additional day off every 2 weeks until "things pick back up again", by starting the conversation you will give them something to think about before they pull the trigger without talking to you first. They may come back with 50% reduction in hours and pay, but that may still be better than the alternative.
Note there is some risk to this. Obviously if they weren't planning on letting you go this could put the idea in their head that they can now reduce your hours. But if you are "highly skilled" and good at your job, the risk of losing hours (or your job completely) should be relatively low if they weren't planning on making a move already. This might also depend on what kind of rapport you have with your manager and/or the decision makers you speak with.