Choosing principal chain in the nomenclature of organic compounds

In this question, I am not sure as to which of the following two chains should be considered as the principal chain.

Approach 1 (7 carbon chain, 2 substituents):

4-methyl-4-(1,1-dimethylethyl)heptane

Approach 2 (6 carbon chain, 4 substituents):

2,2,3-trimethyl-3-propylhexane

Clearly, the carbon chain is the longest in the first approach, but approach 2 has more substituents. In such scenarios, which of the two criteria takes precedence?
I found several conflicting responses on this subject, and would certainly appreciate confirmation. Thanks!

For alkanes it is always longest first.

It gets more complicated for other classes of compounds.

I too thought so. But, this is what I found in the IUPAC Blue Book:

"P-44.1 SENIORITY ORDER FOR PARENT STRUCTURES
When there is a choice, the senior parent structure is chosen by applying the following criteria, in order, until a decision is reached. These criteria must always be applied before those applicable to rings and ring systems (see P-44.2) and to chains (see P-44.3). Then criteria applicable to both chains and rings or ring systems given in P-44.4 are considered.

P-44.1.1 The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43)."

Further, it is stated in P-44.3,
"P-44.3 SENIORITY OF ACYCLIC CHAINS (THE PRINCIPAL CHAIN)
In an acyclic compound consisting of individual atoms, alike or different (an acyclic chain), the chain on which the nomenclature and numbering is based is called the ‘principal chain’. When there is a choice for the principal chain, the following criteria are applied, in the order listed, until a decision is reached.
...
P-44.3.2 The principal chain has the greater number of skeletal atoms [criterion (b) in P-44.3]"

From what I understand, the above excerpts suggest that the number of substituents holds precedence over length of the chain.
Am I missing something here?

Sorry, I think I had misinterpreted this point. The longest carbon chain has precedence over a carbon chain with greater substituents. But, above both of those, a chain with more number of principal characteristic group as substituents is given priority.

"P-44.1.1 The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group [\B] (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43)."

Based on this, I can conclude that 4-methyl-4-(1,1-dimethylethyl)heptane is the preferred name.