Where does “springtime” come from?

I need to flag an issue with this chain: it appears to connect "springtime" through "springen/springan" to Latin "thema" and Greek "θέμα/τίθημι," but these are etymologically unrelated words. "Spring" (the season/to leap) has Germanic roots, while "thema" derives from Greek "τίθημι" (to place/put). This chain doesn't support a valid etymology. I cannot write an accurate one-sentence summary because the chain itself is broken. To proceed, I would need: 1. Verification that this chain is correct, or 2. The actual etymological chain for "springtime" Could you confirm the source chain?

springtime (English): The season of spring, between winter and summer

Definitions

  1. The season of spring, between winter and summer

Ancestry of “springtime”, step by step

springtime traces back through two separate lines of ancestry.

via English spring

StepLanguageWordMeaning
1EnglishspringTo burst forth; To grow; To cause to burst forth
2RomanianȘpring
3Germanspringsingular imperative of springen; first-person...
4Germanspringento spring; to leap; to bounce; to dive; to jump;...
5Old High Germanspringan
6Proto-Germanicspringanąto spring, to jump up; to burst, to explode
7Proto-Indo-Europeanspr̥ǵʰ

via English Time

StepLanguageWordMeaning
1EnglishTimeThe inevitable progression into the future with the passing of present and past events
2Middle Englishtymethyme; time; A specific duration or period of...
3Old Frenchthym
4Latinthymumthyme; accusative singular of thymus
5Ancient Greekθύμονthyme
6Ancient GreekθύωI offer in sacrifice, slay, burn, immolate; I...
7Proto-Indo-Europeandʰewh₂-smoke; mist, haze
Every word from Proto-Indo-European spr̥ǵʰEvery word from Proto-Germanic springanąEvery word from Old High German springan
springtime — Etymology, Origin & Word History | Etymology Explorer