Pretty toxic group of comments up in here.
I'm not a Christian but I'm interested in it (not as a faith to join but as a phenomenon to understand). I'm not coming to this conversation with much baggage.
Looking at what people are citing about Paul and that link to a list of scriptures about relationship with Christ someone posted, I have to say I agree with OP the bible doesn't really talk about a personal relationship with Jesus being something modern worshippers should seek. The scripture that comes closest IMO is John 15
4 Abide in Me, and I in you. As the branch cannot bear fruit of itself, unless it abides in the vine, neither can you, unless you abide in Me.
5 “I am the vine, you are the branches. He who abides in Me, and I in him, bears much fruit; for without Me you can do nothing.
Like if someone I love dies I might say that they live on in my heart (abide in me) but I probably wouldn't say that I still have a relationship with them.
It seems that the bible does not say: "speak to me in prayer and I'll reply in your heart so you can know me, and we'll have a relationship, and that's the most important thing". But I'm not a scholar
So I think the top half of the meme is fairly accurate, but I don't think the bottom half is adequately established. To me it seems that the idea of a personal relationship with a living god was propagated/emphasized by apologists/prosyletizers trying to differentiate Christianity™ from other religions. Bad actors probably do abuse the idea too though.