A hardship withdrawal relates to the plan and not the employer. That said, plans vary in visibility to the employer of plan activity. Employers are not legally allowed to take adverse action toward an employee because of exercise of the exercise of rights under the plan, such s taking a hardship distribution. That is an abstract legal proposition that may not be true in practice.
You were informed how to interact with the plan and your account. It may be that you directly contact a service provider, such as an insurance company or an investment company (e.g. Fidelity, Vanguard, T.Rowe Price) or another type of administrative services plan, or someone at the employer, typically in HR. If you are clueless, then ask some HR representative how you can connect with your account. You may be referred to information materials that explain it to you, or you may be given a direct answer, such as a name and phone number or a website.
You will be asked about the reason for the withdrawal and the amount needed to assure compliance with the hardship withdrawal rules. As mentioned above, your employer may be privy to the information, or not.
I am offering no comment on your thinking about loan vs. hardship. You should rethink, preferably with the aid of a plan representative, if that is available. Generally, hardship withdrawal is a last resort (at least in the view of professionals n the industry) and you may not understand the effects of a loan, even facing the prospect of losing your job, and defaulting on the loan. It is probably no worse than the consequences of a hardship distribution. Some plans do not allow hardship withdrawals if a loan is available to cover the need.