What is the true depiction of the periodic table?
La and Ac have $d^1$ electrons in their valence shells, rather than $f^1$ electrons.

The long table you found looks like that for a several reasons.

The trends going down Sc-Y-La are like those seen in groups 1 and 2. The trend going down Sc-Y-Lu is like that of groups 4 to about 10. Since lanthanide chemistry is basically that of trivalent alkali or alkaline earth metals, this tips the balance in favour of group 3 as Sc-Y-La.

Also helping is that group 4 is the first in which the really characteristic properties of transition metals (variable oxidation states; colour; paramagnetism) are seen. Ditto, same thing happens with group 12, which is why they're shown as post-transition metals.

And there's the lanthanide contraction, which starts at Ce and finishes at Lu. If you show Lu as being a transition metal it mushes the end of the Ln contraction into the d-block.

And there's the periodic law, which says that the chemical elements, if arranged according to their atomic numbers, show an approximate repetition of properties after certain regular but varying intervals. Here, La is the first element after Y that shows the approximate repetition in properties.

This research supports the periodic law outcome:


Glawe H, Sanna A, Gross EKU &amp; Marques MAL 2016, “The optimal one dimensional periodic table: a modified Pettifor chemical scale from data mining”, New Journal of Physics, vol. 18, 093011, https://iopscience.iop.org/article/10.1088/1367-2630/18/9/093011/pdf
Restrepo G 2017, "Building classes of similar chemical elements from binary compounds and their stoichiometries", in MA Benvenuto (ed.), Elements old and new: Discoveries, developments, challenges, and environmental implications, American Chemical Society, Washington DC, pp. 95-110


Both sources point to La being more distinct from the Ln than is the case for Lu.

Finally, if you count the differentiating electron discrepancies in each block of the periodic table, noting the above table has a split-d block, you'll find that an Sc-Y-La table has 12 such discrepancies whereas an Sc-Y-Lu table has 13. The current agreed-within-IUPAC table has 14 differentiating electron discrepancies!

As many people have a hard time accepting the idea of a split-d block, I personally feel that a better solution would be a Sc-Y-Lu table with group 3 being shown as Sc-Y-Lu-Lr and La-Ac. That would have the extra benefit of resolving long-standing discussions about the composition of group 3, which have been going on since about 1982, when Jensen published his paper in JChemEd, arguing for Sc-Y-Lu:


http://www.che.uc.edu/jensen/w.%20b.%20jensen/reprints/018.%20la%20vs%20lu.pdf


Nothing much has to change. Just add a 3 above La-Ac in the f-block, in addition to the one over Sc-Y-Lu-Lr in the d-block.

A chemistry book chapter on this group 3 would make fascinating reading (a good thing given, to date, that group 3 is supposed to be the least studied group).

Hope that helps.