am i really jewish? (from a more cynical point of view)

my mum’s mum’s mum was jewish (making my mum 1/4 jewish) and my dad is fully jewish.

i know this technically makes me fully jewish, but i never really feel comfortable claiming that, since the 1/8th that supposedly makes me jewish feels so distant and insignificant.

given that my dad stopped being a part of my life very young, and my mums side don’t keep any traditions, and i don’t live near a jewish community, would jewish circles actually consider me jewish? and if they did, would they see me ‘barely jewish’ or as less jewish than someone who is fully jewish? would my jewishness be taken seriously or as seriously among other jews? i’m just wondering if i would be accepted, as i don’t want to claim something and feel like an imposter.

thanks for listening !!