The electricity cost argument is really just a side issue - honestly, expect maintenance and wear to cost you more than before.
But real talk, if your commute is wearing you out, you don't even need to do much math: you're saving 20-30 minutes every day, you arrive not completely exhausted, and you're taking it easy on your body.
One thing I've never heard anyone mention - check out the secondhand market or refurbished models from bigger retailers, you can get decent bikes for half the price because tons of people dump them after a year. If 2800€ is too much for you, that's a real way to test if it actually works for you long-term.