Stored Procedure Error on Commit and Begin Statements

Your error handling code is incorrect, as it does not rollback or commit the transaction in certain cases

It also swallows exceptions and instead returns an error code. You are far better off just letting the error bubble up back to the client. You should use SET XACT_ABORT ON to ensure a rollback.

Given that you are only ever executing one statement, you don't even need a transaction anyway

ALTER PROCEDURE [dbo].[UpsertServiceTicket]
    @TransactionType INT,
    @Id INT = NULL,
    @CreationDateTime DATETIME = NULL,
    @Issue VARCHAR(MAX),
    @ReportedDateTime DATETIME = NULL,
    @ResolutinoDateTime DATETIME = NULL,
    @CreatedBy INT = NULL,
    @ServiceRequestNumber NVARCHAR(MAX),
    @Status VARCHAR(MAX) = NULL,
    @IsDeleted BIT = 0,
    @LocationId INT,
    @SubLocationId INT,
    @RequestorId INT,
    @ConfirmedBy INT = NULL,
    @DepartmentId INT
AS

    SET NOCOUNT, XACT_ABORT ON;

    SET @CreationDateTime = ISNULL(@CreationDateTime, GETDATE());

    IF (@TransactionType = 0)
        INSERT INTO ServiceTickets (
                    CreationDateTime
                    , Issue 
                    , ReportedDateTime
                    , ResolutionDateTime
                    , CreatedBy
                    , ServiceRequestNumber
                    , [Status]
                    , IsDeleted
                    , LocationId
                    , SubLocationId
                    , RequestorId
                    , ConfirmerId
                    , DepartmentId
                    )
                VALUES (
                    @CreationDateTime
                    , @Issue
                    , @ReportedDateTime
                    , @ResolutinoDateTime
                    , @CreatedBy
                    , @ServiceRequestNumber
                    , @Status
                    , @IsDeleted
                    , @LocationId
                    , @SubLocationId
                    , @RequestorId
                    , @ConfirmedBy
                    , @DepartmentId
                );
        -- updating the service ticket table
        ELSE
            UPDATE      ServiceTickets
                SET         CreationDateTime        = @CreationDateTime
                            , Issue                 = @Issue
                            , ReportedDateTime      = @ReportedDateTime
                            , ResolutionDateTime    = @ResolutinoDateTime
                            , CreatedBy             = @CreatedBy
                            , ServiceRequestNumber  = @ServiceRequestNumber
                            , [Status]              = @Status
                            , IsDeleted             = @IsDeleted
                            , LocationId            = @LocationId
                            , SubLocationId         = @SubLocationId
                            , RequestorId           = @RequestorId
                            , ConfirmerId           = ConfirmerId
                            , DepartmentId          = DepartmentId
                WHERE Id = @Id;

If you do need a transaction to do a proper Upsert, use this template, with HOLDLOCK, UPDLOCK hints. You do not need a BEGIN CATCH as XACT_ABORT ON will handle the rollback

Use this pattern:

Begin Tran <TransactionName>

BEGIN TRY
   --Some Statements
   Commit Tran <TransactionName>
END TRY
BEGIN CATCH
    DECLARE @Error NVARCHAR(4000)
    SET @Error = ERROR_MESSAGE()
    ROLLBACK TRAN <TransactionName>
    RAISERROR (@Error, 16, 1)
END CATCH