What is the opposite of 'owe'?

I don't think there's a single word that expresses the opposite relationship. But instead of describing the state, you can describe the transaction that implies this state:

Peter lent John $100

However, there could be other reasons why John owes money to Peter, such as Peter performing a service for John, and now being owed the payment, or Peter winning a lawsuit against John.

I understand your question to mean that you wish to retain the same subject - verb - object order in the negative. I therefore suggest:

“I owe you £10” in negative form is “You owe me £10” (reverses subject/object order)

=

“I am entitled to £10 from you.” (Retains subject/object order, as you specify)

Entitled = having the right or permission to do something

“You are entitled to a refund.”

Collins

I owe you $10 -> You are due $10 from me; you are owed $10 by me.

This isn't just a problem with the word "owe." The relevant part of the sentence structure is: subject, verb, direct object. The question implies that there one can construct the opposite, i.e. direct object, verb, subject and still make sense, each a single word. I'm not a grammarian, but believe that this is not possible. John hit Peter. Peter ??? John. Etc.

From a finance perspective:

Peter credited John $100

From https://www.britannica.com/topic/credit:

Credit, transaction between two parties in which one (the creditor or lender) supplies money, goods, services, or securities in return for a promised future payment by the other (the debtor or borrower).

If A owes B something, B indebts A. This is marked in the OED as a rare usage; the Oxford English Dictionary speculates that it is inferred from the adjective indebted (indebt, v.), and early examples use this as the reflexive (meaning to put oneself in a situation of debt):

Now rare.

1. transitive. To bring under monetary obligation; to involve in debt. (In quots. reflexive.)

2. To bring under an obligation of any kind.

Some online dictionaries (like Merriam-Webster) list the term as archaic, but others (Lexico) treat it as current:

Cause (someone) to owe money or an obligation.

‘no generation should be able to indebt future generations’

The word has been used recently in non-reflexive ways:

It is important here to ignore the origin of this gift that never seems to indebt the receiver. (Joelle Vitiello, "Friendship in the Novels of Andree Chedid," Symposium, 49.1, 1995, COCA).

For a long time, some villages refused to accept water or electricity lines, disliking the spiderweb-like intrusion into the earth (where Muy’ingwu, the germination deity, has his dwelling), and foreseeing also that this would indebt them to non-local companies, and compromise their independence. (Peter Whiteley, "The Fire Burns Yet," Aeon, 25 November 2013).

A living donor, for instance, could be motivated [...] by a desire to indebt and manipulate someone else. (Gill and Sade, in Joseph A. Stramondo, "Seeing the forest through the trees: What the radical feminist critique of prostitution can teach us about the sale of kidneys by living suppliers," *International Journal of Feminist Approaches to Bioethics, 6.1, Spring 2013)

The article describes Chinese loans as a 'cunning' device used by Beijing to indebt poor countries and gain control over their strategic assets. (Beyongo Mukete Dynamic, "China's Power in Africa: Rhetoric and Reality." Power, 2019.)

By giving her money, he indebts her. (Karen Murree, Reading Murder in Six Major American Novels, 1994.)

Thus the following usage would be acceptable, even if quirky:

Peter indebts John for $100.

I am 'due' one-hundred dollars means that someone 'owes' you the money.

"is indebted to" e.g. Peter is indebted to John for $100