Pros, cons and use cases of seller finance in M&A

So I got interested in https://www.bbc.co.uk/news/business-55632501 because it mentioned that, as part of a rescue deal, the buyers for a bankrupt retail chain were loaned the capital needed to complete the acquisition by the seller of said chain, Philip Day, the former CEO of Edinburgh Woollen Mill, the main retail chain in question (there were sister businesses that were rescued as part of the acquisition deal).

What are the use cases of seller finance in an acquisition deal such as the above?

Are they just hoping that, if the buyer defaults on the loan, they can take control of the business back while cashing the interest payments, and if the company files for administration, as a major creditor, they can maximise their claims on the company's assets?

Or could it be that they can't raise enough capital to sell their stake in the business, so might maintain a minority stake in the business (I think this might have somewhat been the case with Walmart and Asda, as they haven't completely divested from the business, although I don't think they resorted to seller finance) by lending capital to the buyer to facilitate a majority takeover?

Are they hoping that you can buy them out over time with incoming revenues?

Are the interest payments tax deductible and that's why they do it?

I know a famous example of someone who invested a lot of capital into a struggling business and was able to extract as much value as they could out of said business was Eddie Lambert, CEO of Sears Holdings, whose merger from K-Mart and Sears he oversaw, as he sold off the chain's brick and mortar stores to a REIT he controlled, and sold product brands that Sears owned to other companies, such as a family of power tools to Black and Decker.

Are they just hoping to leverage seller finance to maintain visibility within the business, so that they can dispose of the company's assets and get what value they can, knowing that certain creditors get priority on the company's assets?