It depends more on what you’re looking for, sound-wise, and what your long term intentions are.
On the DAC front, the Bifrost 2 is hard to beat unless you want to spend a lot more (as pure DACs go, the next stops, for me, would be the Chord Qutest or Matrix X-SABRE Pro (MQA). It hits hard, as a nicely meaty presentation, good tonal weight, excellent detail and dynamics. And it’s a longer-term keeper-piece, especially where it is upgradeable.
Amp wise, if you want some tube-flavor and the ability to power pretty much any headphone out there, then the Lyr 3 is a lovely choice. If you don’t want the tube-flavor, then Jotunheim or one of the various THX amps are a good start (though the THX stuff will go better with the Ananda than it will the HD800S), since they’ll run fully balanced out of the Bifrost 2. And if you don’t need quite as much power, and don’t care about balanced input/ouput, Asgard 3 is rather good, too.
Headphone wise …
No, personally, I would not buy the Ananda.
While it is probably the best sounding planar can available at its price point (at least right now, where it’s $699) I don’t find lower-mid level planar cans to be that compelling, and haven’t since the HE-500 and original LCD-2.2c.
That extends to most lower-mid-level planar cans if it has to cover all genres, due to a tendency towards “wall of sound” rendering of really complex music (e.g. big orchestral/classical/operatic pieces). They have other strengths, and the above may not matter if you have more than one headphone and don’t mind using different cans for different genres.
Tonally the HD800S is a side-grade from the Ananda, though the Sennheiser will spank the Ananda hard from a detail, micro-dynamics, stage and separation/layering perspective.
If detail and stage are what’s most important to you, then the HD800S is a definite upgrade, but if you care about other things as well, I’d have the Focal Clear on the list also (you’ll lose the staging there), and I’d have the ZMF Aeolus and Auteur on the list as well as the Arya (though Ayra still exhibits that “wall of sound” effect to a certain degree).
Really, though, if I had the Bifrost 2 and Lyr 3, and wanted an upgrade from the Ananda, I’d probably be leaning either ZMF (if their flavor is your thing) or HEDDPhone - even if it meant waiting a bit longer.
All that said, others can probably better advise you on the mid-level stuff at this point. And they’ll have an easier time of it if they know your musical/genre, tonal and signature preferences.