And yet jump 4 is TL13 in the Third Imperium setting.
This is where we bump up against the cleavage point between the two (well, two and a half...) CT starship paradigms.
LBB2.81 permits J4 as early as TL=10 controlled by a model/4 computer in a 400 ton form factor (or smaller).
LBB5.80 permits J4 at TL=13+ as a limitation of
--> custom <-- drives.
The way to square this circle of differing limitations is to interpolate between them for a "thread the needle" approach.
First ... J4 capability needs to be "discovered, tested, proven" using
custom drives before the necessary design parameters can be back ported/tuned into the capabilities of standard drives.
In other words, there needs to be a capability within the polity/faction of building LBB5.80 TL=13 J4
custom drives and make them WORK before you can then turn around and use that higher tech research and development to enable LBB2.81 TL=10 J4
standard drives to operate in a hull form factor of 400 tons or less.
Basically, "J4 needs to be discovered" (at TL=13) before it can be back ported into older (legacy) technologies (at TL=10) as a matter of tuning up older hardware "to do new tricks" that it was capable of all along (because the engineering margin was there from the start).
Note that such an interpolation between the two design paradigms "preserves the no J4 until TL=13 rule" while stipulating that a particular polity/faction needs to have achieved TL=13 (at a Type A starport) SOMEWHERE within its sphere of control (to make the "research discovery") before that J4 performance (in small hulls!) can be achieved through use of standard drives "properly tuned" thanks to the fruits of the TL=13 research and development discoveries.
One of those "you can teach an old dog new tricks, but you need a new dog to do the teaching first" kinds of deals.
So the world/starport where the construction takes place does not itself need to be TL=13 if using LBB2.81 standard drives (in small enough hull sizes for a small ship universe), while TL=13 is absolutely required to "make the technological breakthrough in the first place" and for building hulls larger than what the standard drives can handle (bigger ship universe stuff).
By the way canonically the Imperium achieved a widespread civilian TL of 13 in the 300s, more than three centuries before the x-boat system was built and actually achieved a widespread civilian TL of 14 before the system was completed.
Which works perfectly fine.
TL=13 was reached 300+ years before the XBoat Networked started build out and was (by the early 600s) a thoroughly vetted and known working technology. Basically, the bugs had been worked out of the necessary systems (on the custom drive side of things relevant to LBB5.80) in advance. So J4 "had been discovered" by the LBB5.80 route already when the buildout of the XBoat network began.
However, by relying on STANDARD drives (rather than CUSTOM drives) for the XBoat Network, the IISS Communications Branch was able to standardize on TL=10 starship designs for the XBoats, rather than needing to standardize around the much more challenging/limited (and presumably vulnerable) TL=13 requirement for custom drives. Use of TL=10 standard drives (A-H) suited their needs just fine and offered a far broader (and therefore, supply chain secure) technology and industrial base for the build out of the Network that wouldn't have to compete with the higher tech demands of other services and sectors (starting with the Imperial Navy).
So custom drives first ... dictates maximum performance limits for standard drives afterwards.