The Chronowarden tree doesn't add a new spell, instead it focused on enhancing and improving every part of the base kit of the spec, making it feel like you're playing the same Preservation you were playing before but faster and stronger.

chronof

The first point and main emphasis of the tree is transforming lf into chronof. This is a bit misleading though: When you spec into it, your lf spell will transform into chronof, however casting chronof sends first a lf to your target, closely followed by a chronof. These are two separate hits that each does its own amount of damage or healing.

chronof still benefits from all the lf bonuses like lfm because it still casts a normal lf. The chronof that hits right after will then do 15% of that lf plus any other damage or healing that has landed on the same target in the last five seconds (up to a decently generous cap, but it does have a cap as mentioned on the tooltip).

The capstone of the tree is then afterimg, which sends up to three chronofs when you cast empower spells. This cap applies regardless of the amount of echoes you might have out: If the base cast of db or sb healed at least three players then those will receive the chronofs, if they healed less than three players then someone healed by an echoed version of the spell might take one up to the cap of three.

fb can't be echoed but the same rules apply: if you hit less than three targets then you will send only that amount of chronofs.

This is a really strong effect because spell ordering means your sb targets will first be healed by sb itself, then by the lf from afterimg, and right after by the chronof which will do 15% of all the previously received healing.

These chronofs can all proc bursts same as a normal lf, and a hard-casted chronof also gives you one stack of tc.

Throughput Nodes

While the main power of Chronowarden comes from chronof and afterimg working together, there are a series of other nodes that greatly synergize with the kit:

reverb increases the healing of your sb even more and improves its healing profile considerably, letting it heal people for a good amount of time after the initial hit.
While haste is not the greatest stat for Preservation, a good free amount of it from primacy will make all your casts after every sb flow better.
imatrix is a really powerful boost to all your empower effects, giving you on average three seconds less on all their cooldowns, meaning you can use them more often and benefit from all the other carrier effects the tree adds to them. With spclarity and this your sb effectively has around ~17 seconds of cooldown which means approximately 50% uptime on primacy.
dtime is an incredibly strong boost to db, almost doubling its total duration in ideal circumstances and allowing you to keep a strong heal over time for much longer and people. The buff to fb is also a really strong component and could mean giving more focus to lower-ranked fbs to get a longer damage over time effect so it has more chances to crit and extend itself.
And maybe the strongest effect, tempburst transforms tts into a powerhouse of a cooldown letting you dish our spells incredibly quickly on demand. Using tts into sb will give you an average of 35% haste during the next 8 seconds, while all your spells also recharge a good amount quicker on top of giving you a lot of movement speed. With this you have a short bloodlust on a 2 minute cooldown.

Gameplay

For gameplay, Chronowarden focuses heavily on lb and then echoing the empowered spells as much as posible:

echoing rank 1 db repeatedly will let you cover the raid on a long-duration powerful heal over time, while in M+ you can keep a really high uptime of two copies of this on the whole group that also does a decent amount of upfront healing on application thanks to afterimg.
To respond to burst damage, our best tool is ramping echoes into consuming them with ve followed by using echo and sb on yourself with four stacks of tc to take advantage of s14p. This will do more total healing than echoing sb directly, as the s14p doesn't transfer to echoes but does increase the lb healing, plus normally chronofs from afterimg are capped to three but by using sb on yourself twice via echo you get healed by two of them and thus transfer all that healing too.
This doesn't mean you won't ever echo sb directly, as sometimes the healing profile offered by reverb can be better than the high burst heal done by lb. This combined with the simplicity and quickness of echoing sb means it is still a tool that you can use on the apropiate scenarios.
Activating tts will grant you a big burst of haste, helping you quickly ramp echoes via manual casts and ta before consuming them with the spell of choice. In raids you will generally use this cooldown as another ramp tool separate from stasis to cover a different damage event, while on m+ it can be used as an emergency cooldown to recover from unexpected big damage or as an offensive cooldown using the extra haste and cooldown reduction to spam faster chronofs.

Another point Chronowarden has over Flameshaper is the fact that all its power comes from buffs to our empower spells and chronof, which means there isn't a single button on a cooldown that drives the power of the hero tree. This lets us freely utilize part of it for damage without compromising our healing.

The free dps increase caused by chronof on filler casts we were doing anyway plus the longer fbs means the spec brings a good deal of passive damage during a normal raid scenario, and the ability to use our new tempburst cooldown on damage instead of healing if we desire gives us a good amount of flexibility.

Conclusions

For all these reasons, the recommended playstyle for Chronowarden is echo, and currently it's the recommended pick for all scenarios in both raids and M+. While on larger raid sizes and not playing correctly it would be very easy for Flameshaper to outperform Chronowarden, proper set ups once you know the fight timings will make Chronowarden a bit more powerfull while also keeping all the flexibility Flameshaper lacks. The gap is close enough that you can play whatever tree you prefer though.

For M+ Chronowarden is ahead in all the metrics that really matter.