] I think Nancy's conversation in Kensington Gardens and Lucy's letter to Elinor in chapter 38 sheds some light on their relationship...

Nancy gossips to Elinor that Edward suggested to Lucy she be released from their engagement due to his lack of prospects. But Lucy would not give ear to such talking.

Lucy in her letter to Elinor says she tried to persuade Edward to give her up yet he wouldn't hear of it- Elinor is shocked by Nancy's eavesdropping but knows Lucy's letter as a falsehood.

Nancy is garralous and tactless. She's somewhat of an embarrassement to Lucy.
On revealing the secret engagement at the Dashwoods, I think Lucy will consider her sister a liability than a confidant.
I wouldn't be surprised if Nancy's blunder and the ensuing uproar permanently impaired any trust the Steele sisters shared.
I agree, afterward they do not appear to be on bad terms and not talking. Hence, the conflicting accounts Elinor received.

At least, the Dashwood sisters can begin to re-new their close bond.
Elinor explains the situation to her own sister. Marieanne is aghast at how much Elinor has been suffering herself the past months while supporting Marieanne through her own grief.

'Marieanne was quite subdued.
"Oh ! Elinor", she cried, "you have made me hate myself forever. Hhow barbarous I have been to you!- you, who have been my only comfort, who have bourne with me in all my misery, who have seemed to be only suffering for me !-Is this my gratitude ? Is this the only return I can make to you ? because your merit cries out upon myself, O have been trying to do it away. "' (ch.37).

Marieanne's confession shows she is deeply moved by Elinor's account- she is divided from Edward forever and deeply unhappy.
Perhaps now, Marieanne recognizes there is nothing unique in her own capacity for suffering.
She now has a better understanding of the nature of her sister, Elinor.

In this matter, Elinor may also take some comfort that Edward made a tactful attempt to end his engagement to Lucy, even though it was not successful.