OP, it's hard to predict what your particular LL will do - not only because you aren't aware of their financial situation, but also because you might not be aware of their decision-making process. It isn't always the case that LL will increase rent in order to maximise short-term profits.
Agents tend to push LLs to increase rent because their fees are a percentage of rent. Agents don't care that this may not be in the LL's overall best interests. So what if the tenants leave? The agent can then charge money for all the extra work involved at changeover. Landlords don't necessarily question the agent's advice. So if your LL doesn't use an agent, the landlord might take a different approach.
From a landlord's point of view, good stable tenants are a huge asset. If you have been there for some time, paying rent reliably and not trashing the house, and you appear to be in a secure financial position, a sensible landlord will want to keep you. Changing tenants is expensive. Finding oneself with a "nightmare tenant" is hugely expensive. I won't increase rent if it means losing my current good tenants.
At the same time, it could be unwise to hint to your landlord that you're struggling with the rent and that you might leave if they put it up by much. If they perceive you are in financial difficulty and there is a risk that your bills may overwhelm you so you become unable to pay the rent, they might just decide to get the ball rolling on pushing you out now so they can try to replace you with "safer" (=higher-income) tenants.
Personally, I do plan to increase rent this year, but only by a modest amount (3%). I hope my tenants will stay for a long time. It isn't viable to leave their rent unchanged over many years, especially with high inflation. If I don't increase rent regularly, but instead wait and bump it up to current market level in say five years' time, they'll get a huge shock. They might be unable to afford that massive jump in rent (bad for them), plus it may well prompt them to leave (bad for me).
However, I realise that many landlords find the idea of raising their sitting tenants' rent so unpalatable that they never do so, preferring instead to wait until a change of tenants. Ironically, that can put tenants in a difficult situation. The landlord may end up hoping the tenants will leave of their own accord, trying to give them a nudge in that direction by allowing the property to fall into disrepair, possibly justifying it to themselves on the grounds that "tenants are getting cheap rent, so it's only fair". Meanwhile the tenants feel trapped in the bad conditions because they are used to the discounted rent and know that moving means a very big increase in their monthly outgoings.
So yes, it's complicated.