IME the means of control of facilities is via the method by which they are booked (and it is perhaps simply more unspoken common sense that non-residents are not entitled to use them?). That would tie with why the LL is requesting the Tenants Facilities-booking-login. After all, if he could legitimately book them himself, why would he need to involve the tenant at all?
Same way the historic garden squares in Notting Hill (per the film etc) are accessible only by those who have a key. And if you own a flat and let it, you no longer have a right to a key.
You could enter into a TA where the LL remains resident, perhaps a flatshare, or even perhaps a 'one room locked' kind of arrangement (though the latter is to skirt HDB rules, IMU). But at what price, vs letting the whole unit together with all the rights that go with it. It'd be a significant price/loss for the LL to pay just to maintain access to the occasional use of the facilities...
Anyway, it's a moot point now. The OP has said that management don't allow it.
