The two greatest commandments are that which all the laws and prophets rest on.
What does it mean, and what does it look like to love the Lord with all your strength?
It means we do that which our Father does as expresses through His Son. In other words, we walk as Jesus walked.
How about loving God with all our heart or pur Soul? The three both center and balance us. This is not simple, and it often goes against our will, and our earthly desires.
Furthermore, It is a given that if one loves the Lord with all their heart, strength and soul, that they have both accepted and Proclaimed Jesus as Lord.
We then get to love our neighbors as ourselves, which is the second greatest command. I would add that as we grow in Christ, our love for the Lord widens and by doing so, we learn to love ourselves the way God would have us, and this spills over to how we love our neighbor.
As Christian's, these two greatest commands are core to our belief and our walk with the Lord and it requires faith, because honestly, the Lord asks us to do some pretty tough things, like praying for our enemies etc. Without faith, we stagnate.
The issue is that most of this commits the fallacy of begging the question. Who the Lord is, is what is important. We simply cannot say it is good enough to love the Lord when one's idea of the Lord is inconsistent with the biblical revelation of who he is.
1Co 8:5 For although there may be so-called gods in heaven or on earth—as indeed there are many “gods” and many “lords”—
1Co 8:6 yet for us there is one God, the Father, from whom are all things and for whom we exist, and one Lord, Jesus Christ, through whom are all things and through whom we exist. (ESV)
Paul is here contrasting the many so-called "lords" with the one Lord. The problem with just believing all we need to do is believe those two commandments, is that it makes us no different than the Jews.
The passage in Romans 10:9-10 has 2 parts.
1. Confess the Lord.
2. Believe in your heart.
If you do not believe in your heart, then ones confession is mute. This agrees with John 3:16.
In summary, it's not about simply believing the two greatest commands, but it's about really believing them by trusting God, and living them out.
Of course the confession and belief work together. The point is rather,
in whom is one confessing? As the OP shows, Paul links confessing Jesus as Lord with confessing him as YHWH, in verse 13.
When we look at John 3:16, we have to consider what it means to "believe in him". Verse 18 gives us a clue:
Joh 3:18 Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not
believed in the name of the only Son of God. (ESV)
And, of course, John 1 provides us with the same:
Joh 1:12 But to all who did receive him, who believed in his name, he gave the right to become children of God, (ESV)
It is believing "in his name," in the name of Jesus, which is the basis of the confession Paul mentions in Romans 8. What "name" refers to is:
"Expressing the sum of the qualities which mark the nature or character of a person. To believe in the name of Jesus Christ the Son of God, is to accept as true the revelation contained in that title." (Vincent's Word Studies)
To "believe in the name" of Jesus then, is to believe in all that the Bible reveals him to be. This then leads back to everything. Salvation is dependent on confessing Jesus as Lord, which according to Paul is confessing him as YHWH, which is consistent with what John says in John 1:1-18.
This is why we cannot and must not say that to be a Christian one simply must love the Lord with all their heart and love their neighbour as himself or herself. That is simply not what the Bible says. This is why we can and
must say that cults such as Mormons and JWs are not and cannot be Christians. They deny the most central reality of Scripture.
To claim they are Christian because they "love the Lord," is to deny the Great Commission, to be unloving by letting them die in their sin. Sure, they "love the Lord," but when contrasted with the biblical revelation of Christ, their "Lord" is one of the so-called "lords" mentioned by Paul--a lord of their own making.