A lot of founders I talk to are confused about where HR sits in their organization. Usually, the hiring of the first full time HR person comes from an acute need: Payroll, onboarding, performance reviews, etc. These are very tactical needs that every business has to address, but it sets the function of HR off on the wrong foot.
There are essentially two orientations of HR (or People) departments in a startup or tech company:
Administrative duties of the people team need to be taken care of regardless of the company's orientation towards HR. It is table stakes and important. Payroll snafus can kill a company. Cultural issues that result in litigation can tie up executives and put financial and legal strain detracting from focus. These things are important, but are typically reactive.
I advocate to founders to think of HR as a strategic competence. The right people leader should be tasked with ensuring that the company has the right human resources to achieve its plans for the quarter or year. In this regard, HR is strategic in the same vain that Finance is strategic: One side makes sure there is runway to continue working towards the vision of the company and the other ensures there are the right human resources to execute on that plan.
HR is actually many different, disparate disciplines rolled under one organization. Some are administrative, but recruiting, L&D and employee experience should be viewed as strategic means to ensure that the company has the right folks, at the right time to deliver on what the organization is seeking to accomplish.
The right people leaders should have a seat at the senior table in the organization. They should be able to push back on commitments by other organizations by identifying talent shortages and limitations on hiring and ramping new talent. Just like when finance pushes back on Marketing's new big ad buy, the people leader needs to push back on overly ambitious product roadmaps by deeply understanding the talent on those teams and what they are skilled in.
An administrative HR leader may have an objective like "Ensure company happiness is at X level" or "Hire X people this quarter". A strategic leader will have an objective like "Ensure the product team has all resources necessary to deliver on their commitments." An administrative leader reports into the COO or CFO. A true strategic people leader reports into the CEO as their right hand (with the finance leader being the left hand).
One final note on HR: They are an agent of the company. Technically, their responsibility is to the the board and the overall governance of the organization. As such, it is wise to handle your interactions with HR with care. Ultimately, they are there to ensure risk is mitigated. When in question, you should seek your own council outside of the company and navigate HR conversations collegially, but skeptically.