Paul's message and authority is of Christ not of his own. He is explicated with this in Gal 1:11-12 "I want you to know, brothers and sisters, that the gospel I preached is not of human origin. I did not receive it from any man, nor was I taught it; rather, I received it by revelation from Jesus Christ." so at the very least what he says in Galatians we can receive it as though it was from Christ. I am not ignoring what Christ said. you have a habit of conflating terms with little support to back it up.
Mat 15:3-4 says "Jesus replied, “And why do you break the command of God for the sake of your tradition? For God said, ‘Honor your father and mother' and ‘Anyone who curses their father or mother is to be put to death.’"
Christ here is referencing the 5th commandment as a commandment of God. There is no argument here. What he is not doing is isolating the 10 commandments and calling only the 10 the commandments of God. This is where your conflation is lacking support. Paul uses this term the commandment of God too in 1 Cor 7:19 and based on it mirror versions in Gal 5:6 and Gal 6:15 his meaning is more analogous with Christ's law. Do Christ and Paul conflict with each other? no, because "commandment of God" is ambiguous and we can't just lump them all together and say they point to the same context. We can say Christ and Paul both are referencing the commandments of God but based on it's use we cannot isolate the commandments of God to just the 10, since Paul clearly is not referencing the 10.
Christ and Paul's goals are different in both accounts. Christ is rebuking, Paul is teaching. Christ's point is to call out the Pharisees and trap them in their own game. He does this in response to them accusing the disciples of breaking tradition by not washing their hands so in like he accuses them of use tradition to overstep law. His point is to expose their hearts, it is not to isolate the 10 commandments and call them God's commandments. With Paul is point to show what is important in Christian living, he does not cancel law but instead emphasizes Christ's law, in doing so it fulfills all law (Gal 2:14). This is Christ's law, which is a heuristic approach to keeping law. Instead of looking at a check list we are to approach circumstances by how we can show love, the outcome of which is lawful so we can put the check list away.
no law is broken, the outflow of Christ's law is only lawful practice. We do not murder, steal, or sleep with our neighbour's wife in the name of Christ's law. these are direct immoral behaviours that are incompatible with Christ's law and it would be silly to say otherwise. When it comes to our behaviour towards God, like idolatry or taking his name in vain then the same applies as Christ's law is regarding loving God as our priority, so no love of God would include idolatry or taking his name in vain. Sabbath is not as easy to know who we are loving by resting, despite the call to obedience, the action called for is not innately moral in action, so it is a bit obscure in how we should approach it (by loving God or loving our neighbour?) most recognize a trend that the first part of the 10 is action towards God, and the last part is action towards each other but the 4th on the boundary so even in this trend it is not clear and we are to conclude that obedience only is the loving part. But Christ tells us that doing good on the Sabbath is lawful (Mat 12:12) so ceasing work is lawful but so is doing good and our labour may be justified through our goodness. In doing this, Christ shows us the goal of the 4th commandment is regarding action to God through obedience as well as action to each other through loving. So there is no breaking commandments, there is only lawful action.
Christ's law does not merely "sum" up the 10. Christ says "all of the law and the prophets hang upon these two commandments" (Mat 22:40) such a statement cannot be reduced to the 10 commandments and as Christ's words state include all the law and the prophets.
James says
IF you really keep the royal law found in Scripture, “Love your neighbor as yourself,” you are doing right. (v8)
BUT if you show favoritism, you sin... (v9)
FOR whoever keeps the whole law and yet stumbles... (v10)
the focus is keeping the royal law. The preposition after v9 "for" (also in v11) shows a relation with the last statement regarding "if you show favouritism" it is intended to expose those who feel they are exempt from certain conditions or that because they so good with one then it covers them with the others which is an inherent risk of numerating a list. The answer is keeping Christ's law, in doing so we don't get trapped into thinking we got most of the laws so should be good but rather if we are calibrated on one law, Christ's law, then there is no balancing act with law.
Let's call a spade a spade here, the issue is not how this relates to commandments 1-3 regarding clear instruction to love God nor is it 5-10 regarding clear instruction on how to love each other, but on the 4th commandment. Because Jesus shows us that doing good on the Sabbath is lawful (Mat 12:12) then we can conclude that a goal of doing good on the sabbath over a goal of ceasing work is also lawful. I get that to you the Sabbath looks a very specific way, but hypothetically if on your way to church on the Sabbath there was a sheep trapped in a pit would it be lawful to pull it out? of course, since Christ tells us this exact scenario. Would it be lawful to turn around and find another way to avoid helping the trapped sheep? If we use the good Samaritan to calibrate our goodness, then avoiding helping others is not an example of loving our neighbour, thus a violation of Christ's law. If we violate Christ's law to keep a law-keeping task list, then we are not actually keeping law, we violate it, which is what James's point is.
So on the Sabbath, if there is a trapped sheep, our duty is to help and in doing so we keep Christ's law, but in ignoring it we violate Christ's law (so it's best to keep it). This is a limited context of pulling sheep out of pits, but is goodness so limited? if there is goodness to be done, we should not avoid it in the name of "ceasing work" as we are also bound by keeping Christ's law to not ignore or avoid goodness. This doesn't mean our action on the Sabbath changes, it just means we shouldn't close our curtains or shut our door to avoid being distracted by doing good things. If we are aligned with Christ's law, then our motivation for all things is also aligned with Christ's law and in that space no law can be violated and all our action inherit lawful action.
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