I have the following output from a mixed-effects linear regression model with an interaction. This model comprises:

1. A continuous outcome (ranging from 590 to 1401).
2. A group variable (binary; control vs. treatment).
3. A continuous covariate (ranging from 0 to 1).
4. An interaction term between a group variable and a covariate.

> summary(test)
Linear mixed model fit by REML. t-tests use Satterthwaite's method ['lmerModLmerTest']
Formula: outcome ~ group * covariate + (1 | subject)
   Data: ex.dat

REML criterion at convergence: 1942.7

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-2.8484 -0.4493 -0.0084  0.3499  3.8192 

Random effects:
 Groups   Name        Variance Std.Dev.
 subject  (Intercept) 20772    144.12  
 Residual              4511     67.16  
Number of obs: 164, groups:  subject, 48

Fixed effects:
                         Estimate Std. Error     df t value Pr(>|t|)    
(Intercept)                833.73      31.85  55.31  26.175  < 2e-16 ***
groupTreatment              20.95      45.08  55.47   0.465 0.643903    
covariate                   66.99      18.68 114.30   3.586 0.000496 ***
groupTreatment:covariate    14.14      26.49 114.39   0.534 0.594531    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

In this case: I believe I can say (+ please let me know if there are any issues with these interpretations.):

1. The covariate coefficient of 66.99 represents the average increase in the outcome for each unit increase in the covariate within the (baseline) control group. (Significant)
2. With each unit increase in the covariate, the outcome is, on average, 14.14 units higher for the treatment group compared to the control group. (Not significant)

However, considering the coefficient and its corresponding p-value of the group variable, I am unsure whether it would be appropriate to conclude that there is no significant difference between the groups.

If I cannot draw such a conclusion based on this model, which model or which number should I examine to determine if there is a significant difference between the control and treatment groups?

Looking forward to hearing from you. Thank you!