[tthflssy]

Without knowing your context, it is hard to give advice, that is ready to be applied. As a manager, you will need to collect and produce data about what is really happening and what is the root cause.

Clear up first what is the charter of your team, what should be in your team's ownership? Do you have to do everything you are doing today? Can you say no to production feature development for some time? Who do you need to convince: your team, your manager or the whole company?

Figure out how to measure / assign value to opex improvements eg you will have only 1-2 on-call issues per week instead of 4-5, and that is savings in engineering time, measurable in reliability (SLA/SLO as mentioned in another comment) - then you will understand how much time it is worth to spend on those fixes and which opex ideas worth pursuing.

Improving the efficiency of your team: are they making the right decisions and taking the right initiatives / tickets?

Argue for headcount and you will have more bandwidth after some time. Or split 2 people off and they should only work on opex improvements. You give administratively priority to these initiatives (if the rest of the team can handle on-call).