You're right! I looked it up in my PIE dictionary, and it mentioned the root words (s)ter- 1 , (s)terǝ- : (s)trē-, although it hardly mentioned other related Germanic languages that equipped this word in their respective shapes. It instead chose to mentioned previous states of the German language referring to conditions of stiffness.
Still, I believe you, it sounds logical to me that the root word translated to alertness (There does not seem to exist any better term), a state of rafraîchissement.
Adjectives don't have tense - they have different forms based on grammatical gender, and number. This is the basic pattern, though there are exceptions:
- singular indefinite en-words use the base form: vacker
- singular indefinite ett-words add a -t: vackert
- plurals and definites use an -a suffix based on the word stem: vackra