The issuance of securities by a company is very similar to how the US Treasury issues bonds. The government may sell their T-bills out on the open market for federal reserve notes (dollars), however they have the option for the federal reserve to purchase them directly in exchange for interest (paid with taxes).

When a company issues stock in their company, they fractionalize the value of their company into these securities and sell them on the open market in exchange for federal reserve notes. Generally this is a fundraising activity with the promise to pay dividends based on the profitability of the company. You might analogize the dividend being paid to the holder of the security as having been paid by the 'tax' or profit that is collected from the company's clientele.

The dividend is like having a variable interest rate on the issued securities based on the 'ability to pay' from profits. The value of a security theoretically is 'backed' by title and interest in the underlying corporation. In effect, the stock is a harder asset than is the present fiat dollar, but is very similar to (if not exactly the same) as the fiduciary instrument that is the dollar. The only difference is regulation around the tracking of trade of the stock. If tracking of trade of a stock in a company were fully public, verifiable and inbuilt to the transference process, like a blockchain, there would be little need to regulate the trade of stocks as every transaction is fully traceable and auditable.

A company may chose to further fractionlize the company by issuing more stock and therefore inflate the supply, or they may perform a split. A split theoretically does not dilute any previously issued stock, but only fractionalizes it to play (and therefore profit) on the psychology of the plasticity-of-value around unit price.

If a company, rather than issuing stock through generation of paper instead issued its stock by means of a cryptocurrency, either through a unique blockchain, or as an NFT, this would obsolete several middlemen around the public stock trade. If the unique blockchain route were chosen, the company could theoretically 'pay' miners to secure its blockchain by issuing stock as a reward for proof of work. Alternately, it could use a proof of stake model where a chain of trust is established around securing the blockchain, but the long-term viability of this method is unclear to me. A proof-of-work security blockchain could have its algorithm periodically modified, though made public and open-source, to adjust the fractionability or total quantity of stock available. The company could code the software such that a particular wallet would always be the origin (other than miner awarded stock) and it is able to sell out of this wallet to a potential shareholder.

How does this relate to the federal reserve? This exercise points out the treasury and federal reserve have many 'aces up their sleeve' to keep the system going. They already periodically adjust the interest rate to suit their ability to pay 'dividends' based on tax revenues, they can issue stock with no need to ever pay it back so long as someone out there willing to 'buy' it by accepting it for goods, and they could even perform a 'split' such that anyone holding a dollar in a US bank now holds two dollars but everyone outside the US does not benefit from this. This has also been done during covid with the government issuing 'covid checks'. These analogies likely extend with other tricks companies use to manipulate the value of their stock such as stock by-backs.

I hope this helps you understand that the government operates much more like a business than you might imagine, and that businesses through issuing stock are engaged in a form of currency creation.