As already stated, openHAB and openHABian do not do anything about IP addresses. DHCP does.
So turning a router (= DHCP server plus default gateway) permanently off is just a bad if not to say dumb idea, let alone for the (non- !) savings this gets you.
And untested of course as noone else would ever do. Don’t expect others to help you with that - sorry.
And you asked for help without stating that you want the router to stay off in the first place, plus quite some more at first misleading information, making all of us victim to the XY problem.
If you ask volunteers for help, you should be willing and able to follow a minimum of rules such as these.
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