How to track money used for shared expenses against a personal loan?

You can't, on purpose. That's the point of double-entry. You can use a Dollar to pay back a loan or to buy a steak, but you can't do both. You could try to debit from your groceries account to credit the loan, but then you'd end up with a lower number in groceries than what you actually spent at the store.

If instead you use a simple loan payback using Dollars, and then share the expenses, it would work as you want.

I'm in a similar situation-- a house purchase with unequal initial investments in the down payment, with the intention to resolve the inequality over time. There are two items that are think are relevant to your situation which may make things clearer. I am not an expert on double-entry bookkeeping, so I apologize in advance if this advice isn't focused properly on what you're after:

This is awkward to do precisely with ad hoc spending

It's very difficult to say what spending would have occurred with or without this debt, and you might not be on the same page with what spending should count (you may have a system for dealing with this already). If, for example, your fiancé is not all that interested in repainting, but you are, you buying paint may not be the offset you're hoping for. Why should you paying 100% of the cost for paint that your fiancé doesn't want and wouldn't buy satisfy a cash debt you owe to your fiancé?

This is kind of a silly, small example, but it (hopefully) demonstrates some of the issues with taking a highly structured debt (unequal equity in a house) and repaying it in a very unstructured way. It's made a bit worse with undefined fractions of ordinary, unavoidable purchases (like groceries)-- is 100% of the cost of grocery trip A a always meaningful balance for 0% of the cost of grocery trip B? Maybe, but not always. Paying down your debt to your fiancé is not a household expense. It is a personal expense of yours.

You need more categories

As I understand the accounts book you've laid out, you are wanting individual entries to cover multiple things (ordinary expenses as well as your extra household contributions against the debt) and be recorded in multiple places (the purchase itself and also the "extra" money directed against the debt).

But if you have additional categories or subcategories for spending you can track those things while also enjoying the clarity of the double-entry approach. If your heating bill is $200, and you would ordinarily split the cost evenly, it could be represented as Heat (Total) = $200 and recorded as Heat (Logarr's Portion) = $100, and Heat (Logarr's Extra Payment Against Loan) = $100.

The two subcategories add up to the total category amount but explicitly break out the portion of your payments which cover your ordinary portion (what you would be paying if there were no debt to service) and your extra portion meant to offset the debt. There is no ambiguity about what money was directed to which category or purpose.

I, personally, like the idea of fixed payments against what you currently owe to your fiancé with regard to the house because that is clearer. Especially if you spend the money in a way that makes your equity in the house obviously more equal over time (so, if you each pay 50% of the mortgage, you making extra payments on top of that against the principal directly adds to your share of the house's equity in a way that the cost of a dinner out would not). But that sort of approach may or may not suit you for any number of reasons.