I'd say this because of the use of the words and the order they are used in. At the beginning of the poem, luminous and treasure describe the woman in the poem positively, whereas closer to the end of the poem, Edgar Allen Poe starts to say that the woman was lying and it was all a riddle, hinting towards this with the words, 'search', and 'lose'.
A hyperbole is an exaggeration that is not meant to be taken literally. It is usually used to make a persuasive point or to add emphasis. In this case, "opening a door to eternal tyranny" is an example of an exaggeration of this type. While it is likely that tyranny will not be eternal (the country itself will not be eternal), its purpose is to emphasize the risk of keeping the seat of governent vacant.
I shall be telling this with a sigh Somewhere ages and ages hence: Two roads diverged in a wood, and I – I took the one less traveled by, And that has made all the difference
