Hi Claudiu1,
The trick is to format both Date and utcNow() to 'MM-dd'.
But you can't format date within Get Items query filter as date value will be get at query run time while power automate expression are evaluated before action runs the query.
So you have to use a Filter Array action with "value" dynamic content from Get Items as input. Then filter according to your need.
Here a small flow to illustrate, it gets items from a list then filter result having items Created 2 or 4 month later from now (October and December) :
My formula is : @Anonymous(equals(formatDateTime(item()?['Created'], 'MM'), addToTime(utcNow(), 2, 'Month', 'MM')),equals(formatDateTime(item()?['Created'], 'MM'), addToTime(utcNow(), 4, 'Month', 'MM')))
As formula is a complex one you'll have to enter advanced mode edition of the action :

You get this :

Replace empty equals formula proposed by yours :

Filter array now returns only items created on October or December regardless of the day or year.
Your query should look like this : @And(greaterOrEquals(formatDateTime(item()?['Date'], 'MM'), convertFromUtc(utcnow(),'Eastern Standard Time','MM-dd')), lessOrEquals(formatDateTime(item()?['Date'], 'MM'), addDays(convertFromUtc(utcNow(),'Eastern Standard Time','yyyy-MM-dd'),30,'MM-dd')))
Where 'Date' is the internal name of the field on which you want to test the date.
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