Categorical variables in fixed effects model

I am doing a research on factors influencing firm performance, So I am fitting a fixed-effect modelling approach in R using 3-year panel data, with a total of 193 firms, these firms are grouped into 4 different sizes (Medium, Small, Very Small and Micro depending on thier annual sales levels). I need assistance on the model output as results differ when I change the fixed effect. At first (fe (1)) I fitted my model using the individual firms as the fixed effect and then used firm size as the fixed effect and results are quite different, with the second model (fe (2)) showing some dummy variables that are even significant in the model as per below:

fe = plm(LogSales~LocU +Prod+GendreM +Age+PEMP+TEMP+TEMP2+LogTA+
CoAge.TA+AGE2+Web+CoAge+CoAge2+DigMkt+Reg+PMI+UMP+CPI,
index = c("Name"),data = y, model = "within")

- Estimate Std. Error t value Pr(>|t|)
Prod 1.1245e+00 7.8360e-02 14.3502 < 2.2e-16 ***
Age -2.0335e-03 7.8885e-02 -0.0258 0.9794480
PEMP 1.1028e-02 1.8099e-03 6.0928 2.805e-09 ***
TEMP 2.7000e-02 7.3999e-03 3.6487 0.0003017 ***
TEMP2 -1.3478e-04 9.2465e-05 -1.4577 0.1457826
LogTA -2.0082e-01 1.4691e-01 -1.3670 0.1724730
CoAge.TA 2.3592e-01 1.4590e-01 1.6170 0.1067459
AGE2 -1.4893e-04 8.5131e-04 -0.1749 0.8612233
CoAge -7.5364e-01 2.3532e-01 -3.2025 0.0014812 **
CoAge2 -2.6180e-05 3.0207e-04 -0.0867 0.9309830
PMI 1.7307e-02 1.4040e-02 1.2327 0.2184908
UMP -7.7031e+00 2.5110e+00 -3.0678 0.0023168 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(in this output all dummy variables as I would have expected are not even appearing in the output)

Now lets turn to model where I used size as fixed effect:

fe (2) = plm(Logsales~LocU +Prod+GendreM +Age+PEMP+TEMP+TEMP2+LogTA+
CoAge.TA+AGE2+Web+CoAge+CoAge2+DigMkt+Reg+PMI+UMP+CPI,
index = c("Size", "Year"),data = g, model = "within")

P.S: Please note that some firms changed sizes over the three year period (as sales levels either dropped or increased), so I am not sure if that's the reason as to why I got results in which some dummy variables are significant in the model- (all variables with a D. are dummy variables):

Estimate Std. Error t value Pr(>|t|)
D.Loc -1.3370e-01 2.0638e-02 -6.4783 2.062e-10 ***
Prod 8.8848e-01 1.0279e-01 8.6435 < 2.2e-16 ***
D.GendreM 5.5016e-03 3.9366e-02 0.1398 0.8889028
Age -3.7597e-02 6.1833e-03 -6.0805 2.243e-09 ***
PEMP 1.1429e-02 3.0836e-03 3.7065 0.0002314 ***
TEMP 2.7777e-02 9.9562e-03 2.7899 0.0054555 **
TEMP2 -1.5346e-04 8.1031e-05 -1.8938 0.0587718 .
LogTA 5.0778e-02 4.6835e-02 1.0842 0.2787596
CoAge.TA 6.6991e-02 7.4195e-02 0.9029 0.3669664
AGE2 4.4356e-04 8.7201e-05 5.0867 5.007e-07 ***
D.Web -1.9339e-02 4.2966e-02 -0.4501 0.6528251
CoAge 2.3474e-03 7.5914e-03 0.3092 0.7572679
CoAge2 -2.7249e-05 6.3748e-05 -0.4274 0.6692235
D.DigMkt -2.3131e-01 1.6597e-01 -1.3937 0.1639661
D.Reg -1.3983e-01 4.8622e-02 -2.8759 0.0041854 **
PMI 2.3580e-02 2.1768e-02 1.0832 0.2791870
UMP -1.5999e-01 1.5307e-01 -1.0452 0.2963813
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Now I wanted to know if it's alright to go with the second model fe (2) (with dummy variables) and make my conclusions based on it. From variables econometric articles I have consulted it seems it's impossible to have time-invariant variables significant in the model. So I am not sure if the movement of firms across sizes influenced these variables and whether it's fine to work with such results.
Your assistance is appreciated